I get **ΣF = m*a** and gravity pull is **m*g**
But I was once told that there is no reason that the mass in both cases are the same. However, they happen to be according to our most precise measurement. Why wouldn’t they be the same? Can anything have different mass in regard of the context?
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Your question is vague. Are the two formulas depicting the same object in the same situation? Then the answer is an absolute yes, except if it’s a continuum of great size.
In general, of course, those two can be describing completely different objects and situations.
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