两者之间有很大的不同，be able to 是指主观上有这种能力 can 是指客观上你能这么做，或被允许这么做

Also, "can" is often used to ask for permission. "Can I borrow your pen to write this down?" This is improper grammar (The correct way to say it is "May I borrow..."). but people still say "Can I" instead of "May I" all the time :D

Can is similar to to be able to, but to be able to needs to be changed in some instances. For example: "Can I do this?" is the same as "Am I able to do this", but "I can do this" is the same as "I am able to do this".

can and be able to do。同じ意味だよ。でも、「can」は日本語で「～ことができます」例えば[I can read chinese]僕は中国を読みことができますね！。「be able to do」ちょっと難しいだよ、例えば：I will be able to do something...Most of the times,We use(Will)before!例えば： I will be able to do my homework!

I can do it = PERMISSION – human authority / rules and regulations allow me to do it. I can do it = POSSIBILITY – external circumstances allow me to do it. I can do it= ABILITY - inherent properties allow me to do it. (There are times when these meanings overlap.) So, Can you help me with my homework? PERMISSION: will mum, teacher, the examiner allow it? POSSIBILITY: if you don't have anything else to do. ABILITY: are you clever enough/have you got knowledge of the subject ................ The thing to ask is whether be able to also have the same meanings: Are you able to help me with my homework? PERMISSION: will mum, teacher, the examiner allow it? (Seems to be OK) POSSIBILITY: if you don't have anything else to do. (Seems to be OK) ABILITY: are you clever enough/have you got knowledge of the subject? (Seems to be OK) .......... So, up to now, it seems as if both convey the same meanings. ........ states (fact), be able to is normally preferred. "Most people worked harder than me during the University, of course, and when it came to the exams, they were able to draw not just upon two weeks of knowledge. They were able to draw upon three years of knowledge". ..