They convey different things.
I'm in love with Betty.
I have feelings for her. Betty's state of mind is not addressed here.
You could infer that I have intentionally omitted Betty's state of mind, because I am indicating that she does not love me back. However, that is an inference, and not directly stated.
It's possible that Betty loves me, or doesn't love me. You can't know that. All you can know is that I love Betty.
Betty and I are in love with each other.
In this case, I am expressing that Betty loves me back.
However, this still does not mean that Betty and I are in a relationship. Maybe we're both married to other people, even though we have now fallen in love with each other.
This sentence could at best imply that Betty and me want to be in a relationship. Although even that is not a guarantee.
You could potentially infer from this statement that Betty and I are currently not in a relationship (yet). But again, the statement is true regardless of whether we are in a relationship or not.
Betty and I are in a relationship
Betty and I are dating
Betty and I are together
These sentences do explicitly state that Betty and I are in a relationship. Now, it is no longer implied; but stated directly.
However, this does not inherently mean that Betty and I are in love with each other. You'd assume that being in a relationship means that you love each other, but it's not inherently required.
To give you an easier example, compare these two sentences:
I work in healthcare
I like working in healthcare.
While you would expect someone to like the work they do, that is not automatically the case.
It's perfectly possible for someone to work in healthcare and hate their job; or to like working in healthcare without currently working in a healthcare profession.
When interpreting these statements at face value, none of these are interchangeable. They all state different things.
From context, it is possible for intentional implications (or wrong inferences) to add meaning. However, that is specific to the context in which it is said; I can't accurately comment on that based on your question as it is currently phrased.