I found a table at this page that seems to be labeling Vし・Vせず・Adjなく・Nに as present tense, and Vして・Vしないで・Adjなくて・Nで as past tense. Please teach me about this distinction in the above words.
They seem to be attempting to draw a distinction between sequential coordination forms and simultaneous coordination forms.
し・せず・なく・に are (theoretically) simultaneous coordination. The state/action they describe is true/occurring while whatever next thing is true/occurring:
He read a book and watched television (at the same time).
して・しないで・なくて・で are (theoretically) sequential coordination. The state/action they describe is true/occurring before whatever next thing is true/occurring:
He read a book and (then) watched television.
In modern Japanese the distinction mostly isn't bothered with, though, and instead the differences work out something like this:
し is literary (書き言葉) / して is colloquial (話し言葉)
せず (/しなくて) is 'without doing' / しないで is 'instead of doing'
なく is literary / なくて is colloquial
「Xに、」 isn't really used as 'is X, and' in modern Japanese / 「Xで、」 is
(though correct me if I'm wrong, I'm not as sure on the last two)