So I have been a bit lost in the terms, so first of all I present you what I have learned so far:System requirements specification - what users want, what the system should doFunctional requirement - how the things, which users want, will actually work in the applicationAlso I would say that the latter is a design document. Is that right or is there another document in addition to these?
Is functional spec a design document?
testing;documentation;terminology
Functional specification is a design document - describes exactly the functionality of the system. What John Bode suggest is something else, system specification in OP's context means a specification of the software system, done by business analyst.System requirements specification describes the functionality of the system as wanted by users.