"Can" is one of the most commonly known modal verbs (also known as modals or modal auxiliary verbs) used to talk about possibilities, ask for or give permissions, request something, etc. We use can to refer to the present and the future. Have a look:

"Be able to" is a verb phrase. We use "be able to" to talk about abilities. The presence of the auxiliary verb "be" allows us to use the phrase in both present and past tense.

We use "can" and "be able to" to talk about abilities, knowledge, or talent. We use "can" to talk about the present and the future. "Be able to" is used in all tenses to show ability. For example:

When we want to make negative sentences, we use "cannot" and "not able to" or "unable to." For instance:

"Can" is a modal verb that is used to give additional information about the function of the main verb. Have a look:

"Be able to" is a phrasal verb. A phrasal verb is a phrase that functions as a verb. Take a look at the following example:

"Can" is a modal verb and we cannot use two modals in one sentence at once. In this case, we use "to be verb" since we can use it with other modals. Have a look:

We use "can" and "be able to" with tenses:

We cannot use "can" itself to talk about the past. Instead, we use "could. "With "be able to," we use the past tense of the auxiliary verb "be": was/were. Take a look at the following example:

We can use both "can" and "be able to" to talk about present abilities. "Can" is more common than "be able to." Here are some examples:

We use "be able to" to talk about having an ability in the future. This ability is not available right now and will only be achieved in the future. For example:

We use both "can" and "be able to" to talk about future decisions and arrangements. Have a look:

Both "can" and "be able to" are used to make questions.
"Can" is simply inverted to create questions. Watch:

To make a question with "be able to," we invert the "be" and do not change the position of "able to." Consider the following examples: