As I'm interested in this, I've done a bit of research. I'm afraid the first thing that has to be discussed is taxonomy.
THE PROBLEMS OF TAXONOMY
The meaning of simile many sources give vis a vis metaphor and how they're related are not consistent. For example many sources separate simile and metaphor to the point that they're separate things. However, on the other hand, Wikipedia, DailyWritingTips and wiseGEEK say that simile is a type of metaphor. DailyWritingTips goes as far as saying:
In a sense, all language is metaphor because words are simply labels for things that exist in the world. We call something “a table” because we have to call it something, but the word is not the thing it names.
Encyclopaedia Britannica seems to distinguish simile and metaphor more than other sources like Wikipedia:
In the simile, unlike the metaphor, the resemblance is explicitly
indicated by the words “like” or “as.”
If you look up the definition of simile in dictionaries it often says "compare metaphor". This would suggest that they're in different categories, and so separate. But not necessarily, as a member of a subcategory can also be a member of the category that contains the subcategory. For example, The American Heritage Student Science Dictionary's definition of "monkey" begins with some incorrect description, followed by this:
Baboons, macaques, mandrills, and marmosets are monkeys. Compare ape.
Here we see the use of "compare" much like we see in other dictionaries in the "simile" definition. But despite this use of the "compare" note in the definition, monkeys and apes can be considered primates and mammals. With this in mind, whether the "compare metaphor" notes in "simile" definitions means they are separate things is unclear to me.
Just as an illustration of how confusing all this can be, consider the following. It took much time to finally strip Pluto of its planet status. It's now a dwarf planet, which the IAU doesn't consider a planet, much in the way zoology taxonomists don't consider the king cobra a real cobra. Same goes for the red panda and mountain goat. If you search for "Pluto planet again" you'll see a number of articles and videos, ranging from 2015 to 2018 (from what I've seen), about the debates surrounding this issue. It's possible the IAU may change its definition of planet in the future. Beginning just this year (2019) Avogadro's constant will have a new definition.
TRYING TO ADDRESS YOUR QUESTION
Sources claiming that similes are a type of metaphor tend not to explain satisfactorily (in my opinion) how this is the case. In the Wikipedia article for metaphor, it says:
All the world's a stage
This quotation expresses a metaphor because the world is not literally
To me this seems to imply that the condition of being non-literal is necessary for a metaphor. If this is true, and a simile is a metaphor (as they claim), and:
This surface is like an ice block.
...is a simile, the argument breaks down, because there's nothing non-literal about the above simile necessarily. It just says that the surface (literal) has characteristics similar (literally) to those of an ice block (literal), ie., smooth, cold, hard, nothing necessarily metaphoric about it. So in my opinion similes can be metaphors, and probably mostly are, but don't have to be.
In many places you'll see the difference between metaphor and simile described in a way that a metaphor is along the lines of "A is B", whereas a simile goes like "A is like B", or some variant of that. One source that seems to make this argument is Merriam-Webster Dictionary:
Simile vs. Metaphor
Many people have trouble distinguishing between simile and metaphor. A glance at their Latin and Greek roots offers a simple way of telling these two closely-related figures of speech apart. Simile comes from the Latin word similis (meaning “similar, like”), which seems fitting, since the comparison indicated by a simile will typically contain the words as or like. Metaphor, on the other hand, comes from the Greek word metapherein (“to transfer”), which is also fitting, since a metaphor is used in place of something. “My love is like a red, red rose” is a simile, and “love is a rose” is a metaphor.
wiseGEEK also seems to make this argument. It says:
A metaphor compares one thing to another by stating that the first thing is equal to the second. "Her hair is the sun," is a metaphor, while a simile simply states that her hair shines like the sun.
But wait, that explanation seems like nonsense:
- A metaphor is "stating that the first thing is equal to the second".
- "A simile is a type of metaphor". (they also claim this)
- "Her hair shines like the sun" is a simile.
The supposed simile in (3) is "Her hair shines like the sun", not anything meaning "is equal to" the sun. So if (1) and (2) are true, (3) can't be a simile. Alternatively one of the other propositions must be false. So I find this also unsatisfactory.
Many sources make this simplified argument, that a simile is "A is like B" and a metaphor is "A is B".
quickanddirtytips and grammarly.com make this argument. In fact if you look at any online source that tackles this question, it primarily illustrates the differences between the two in this simplified way, including DailyWritingTips.
Instinctively I felt this was correct. After all, examples we get from dictionaries highlight this simplified dichotomy:
The city is a jungle
She is like a rose.
Random House Kernerman Webster's College Dictionary
But it's more complicated than that.
For metaphor to have a meaning that goes beyond the simple "metaphor/simile" dichotomy given so often, we just need to show that metaphors are not just "A is B", as opposed to similes, which are "A is like B" (or variants).
This is actually easy to do. In Christianity "Lamb of God" is a metaphor for Jesus Christ, because the lamb is associated with a sacrifice, and Christ was sacrificed (or sacrificed himself, depending...). The same goes for any other story, be it film or anything else. If you see a personification, that's most likely a metaphor. The dude in the hooded black robe holding a scythe is a metaphor for death. So is Brad Pitt in that movie.
So I hope I've shown how "metaphor" is more of an overarching term, to which belong more specific rhetorical or literary devices. For example Wikipedia asserts that metaphor either contains the following devices or that they are types of metaphor:
I'm not personally endorsing this list. DailyWritingTips says "simile is only one of dozens of specific types of metaphor." I haven't researched this and have no intention of...doing such...thing.
An example of hyperbole as metaphor:
I tried it a thousand times but I can't get it right.
(thousand times might be hyperbole, and metaphor for I tried hard, or many times).
Analogies are a more general thing. They're basically a comparison between things.
2.similarity or comparability: I see no analogy between our situations.
Random House Kernerman Webster's College
It seems to me many analogies aren't similes or metaphors. For example, this is an analogy:
- If you want an idea of how hard it is to fly a helicopter, imagine juggling three tennis balls while chopping onions.
(not a simile or metaphor, as far as I can see, simply a comparison made)
Whereas some analogies seem to definitely be similes:
- Arguing with you is like trying to nail jelly to the wall.
Which is (according to various sources also a metaphor).
I wish I could draw a chart like the pretty one you have in your question that shows where exactly similes, metaphors and analogies lie. There's two problems with doing this (maybe more):
1) I don't think I know what I'm talking about it.
2) The meanings of the three terms are inconsistent from place to place (the taxonomisation problem I mentioned).
However I'll try to give a couple of opinions.
- All similes are analogies. To the extent that similes compare two things, they are analogies, because that's what analogies are, comparisons.
- I think whether something is literal or not either weighs heavily on or decides whether something is metaphor. If this is the case, I think terms such as "figure of speech" or "figuratively" are involved in deciding whether something is metaphor.
- My opinion is that although similes can be, and probably mostly are metaphors, they don't have to be (see the ice block example).
On the topic of literalness, I remember a question on this site about what "literal" means, and though we journeyed through subjects such as the meaning's chronological primacy, and original etymology, I don't think that was answered satisfactorily. My point is we have just another factor contributing to the mess of delineating what is what.
So yeah, I'm afraid I don't know the answer to your question.