'Will' and 'be going to' are two forms of the expression of the future in English (and there are others). They can both be called 'future tense'.
USUALLY, 'will' expresses a simple expectation of what should occur, based on present understanding: 'I will help you tomorrow' because I know that I have free time and have the expertise to do so.
'Be going to' generally expresses the fact that the speaker has internal or external evidence for the future event: 'I'm going to help you tomorrow' because I have a plan now to do so.
In many cases, the two forms are interchangeable, as here.
'Finish' is in the simple present, because the speaker is currently 'finishing'; it could equally well be expressed as 'as soon as I have finished' or 'as soon as I am finished'.
Sorry, I do not understand your reference to 'is going on'. Could you clarify this?