Generally, a term is more rigid and finite than a period.
2a : a limited or definite extent of time; especially : the time for which something lasts : duration, tenure [term of office] [lost money in the short term]
Examples: academic term, term paper, term life insurance, to carry a baby to term
a : a portion of time determined by some recurring phenomenon
Edit to address OP's question edits:
Is it possible to use one or both of them when we describe a point in
time (We have time till 1st of December so we have to finish the
project within this term/period)
You could say we have a December 1st deadline, so we have to finish the project within this period (between now and December 1st). What you will often see instead of period here is time frame:
: a period of time especially with respect to some action or project
The second part of your question:
and when we describe duration (We have two weeks so we have to finish...)?
...within this period or ...within this time frame are a better fit than term.