Can and Able

What is the difference?

How do I explain it to a beginner?

Thanks in advance.

[Tdol]

'Able' is often used when referring to a single occasion.

[blacknomi]

http://dictionary.reference.com/search?q=able

Usage Note: The construction able to takes an infinitive to show the subject's ability to accomplish an action: We were able to get a grant for the project. The new submarine is able to dive twice as fast as the older model. Some people think it should be avoided when the subject does not have an ability, as in sentences with passive constructions involving forms of the verb be: The problem was able to be solved by using a new lab technique. The reasoning here is that since the problem has no ability to accomplish an action, it is not able to do anything, and therefore able to should not be used. Presumably this ban would apply to similar words like capable and to negative words like unable and incapable. In such cases one can usually avoid the problem by using can or could: The problem could be solved.... Keep in mind, however, that passives with get ascribe a more active role to their subjects, and here one can use able to: He was able to get accepted by a top law school.

[blacknomi]

What can you see?

I can see a mouse.
I am able to see a mouse. ( This sounds like he might have bad vision and is stressing the ability of seeing a mouse is not that an easy task.)