What is the difference in being physically capable and physically able?
When would one choose one over the other?
One main difference is the preposition that usually follows each of these words. Typically, you see able to, but capable of.
Other than that, pick a dictionary, look the two words up. I'm citing Collins:
1. having the necessary power, resources, skill, time, opportunity, etc, to do something ⇒ able to swim
2. capable; competent; talented ⇒ an able teacher
3. (law) qualified, competent, or authorized to do some specific act
1. having ability, esp in many different fields; competent
2. able or having the skill (to do something) ⇒ she is capable of hard work
3. having the temperament or inclination (to do something) ⇒ he seemed capable of murder
You can see a lot of overlap, particularly with definitions #1 & #2 for capable, and definition #2 for able. Both words mean competent; plus, able means capable, and capable means able. This means there will be several contexts where either word could be used:
Sammy is an able electrician; I would recommend him.
Tammie is a capable electrician; I would recommend her.
Evan has shown he is able to reach the green from the tee box.
Kevin has shown he is capable of reaching the green from the tee box.
However, the definitions also show instances where one word couldn't be exchanged for the other:
I have to catch a flight; I won't be able to hold the meeting this afternoon.
⇒ This is able Definition #1; capable is not appropriate here.
Because I didn't apply in time, I won't be able to start college this fall.
⇒ This is able Definition #3; capable is not appropriate here.
Melvin is a lazy student; he isn't capable of finishing college.
⇒ This is capable Definition #3; able is less appropriate here.
Dorothy doesn't know what she is doing; she isn't capable of holding the meeting today.
⇒ This is capable Definition #1; but able might be appropriate here.
They mean the same thing, but when there's a further qualifier, capable is preferred, whereas able is usually by itself:
He is physically able. — [normal]
He is physically able to lift 200 kg. — [OK, not that unusual]
He is physically capable. — [unusual, but not wrong]
He is physically capable of lifting 200 kg. — [normal]
There is a difference between being "able to do something" and being "capable of doing something", as the sentence illustrates:
Everyone is able to kill,
but not everyone is capable of murder.
however, when adding the adverb "physically", the difference is filtered out.
To be capable of doing something, you need, first to be able to do it, next the mindset allowing you to.
I agree with most of what has been written. Capable and able mean the same in many situations, but have differences too. This isn't too common in English, but is found in other languages. For example conocer and saber in Spanish both mean "to know" they are interchangeable in some situations and exclusive in others.
One difference I have observed between able and capable is their implied usage or frequency. Capable is more often used to describe hypothetical or theoretical action where able is more often used to describe an immediate or continuous action.
A security guard is able to stand in place for up to 8 hours (implies the guard does this routinely). A security guard is capable of defending others from a violent attacker (implies the guard could do this if needed).
If you switch them around it makes less sense.
A security gaurd is capable of standing in place for up to 8 hours (implies they don't routinely do it though). A security guard is able to defend others from a violent attacker (implies this happens routinely).
Capable is more of a mentality. Able is more of a physical idea. You can be mentally capable of describing the object in front of you; you can be able to lift the 100 lb weights. However, the words are nearly interchangeable anywhere. Even in the examples I gave, the other fits, but one seems more appropriate than the other commonly.
The answers so far all deal with the question from the human angle. I'm more interested in the usage when talking about other things, for example in a text I am revising right now: The authors used "...cell types have various origins and are not capable of differentiating into..." - But I am thinking about changing (editing) it for "able to": "cell types have various origins and are unable to differentiate into ...", mainly because I'm not always keen on -ing forms.