Do always and all the time mean exactly the same thing in these sentences?
Why are you always so busy?
Why are you so busy all the time?
Always itself means all the time. So, both of them are very much interchangeable in usage.
They both mean that the person is very busy on many different occasions.
Although in most cases they can be used interchangeably, like in the sentence you have mentioned, there are some cases where always is more appropriate e.g.
Always be prepared.
"Be prepared all the time" does not sound as good, I think, because always denotes perpetuity or continuity while all the time means repeatedly on multiple occasions. I cant think of an opposite case, where always cannot replace all the time so i guess always trumps all the time.
"Always" is used when a person is regarding time and event conjunctly; "all the time" is used when regarding time only, without regard to the event taking place at that time.