Hello Pink Star,
If you do something 'as soon as possible', you do it as soon as you can.
If you say that something happens "as soon as "something else happens, you mean that it happens immediately after the other thing.
The other thing here is " your ability to do it".
" I am busy working now .I will call you as soon as possible."
I will call you immediately when I can do that; when I finish my work and I am not busy anymore.