'CAN' is an auxiliary verb, a modal auxiliary verb. We use can to: talk about possibility and ability, make requests and ask for or give permission. For instance: She can speak Spanish very well. Can you be quiet! Can I smoke in this room? 'BE ABLE TO' is in contrast to 'can' not a modal verb. It is simply the verb 'be' plus an adjective ('able') followed by the infinitive. We sometimes use it instead of can and could to talk about ability.

They're pretty much the same. There are only two differences that I can think of: -'Can' is an auxiliary verb and 'able' is not (but 'be' is). -'Can' is also sometimes used in requests (although 'could' is politer) ex. "Can I please...?". If you say "Can you..." instead of "Are you able to...", people might think you're asking them to do something.

"Can" is slightly more informal.