Give a speech vs. Make a speech

Both are ok.

A speech is often a part of some kind of event and may be quite short (hopefully ).
In those circumstances it has a purpose related to the event. Opening/closing something, welcoming/thanking people, etc.

BNC:
give a speech - 9
make a speech - 37
give a talk - 28
make a talk - 0

COCA
give a speech - 203
make a speech - 134
give a talk - 60
make a talk - 4
Interesting.

BNC - British National Corpus

COCA - Corpus of Contemporary American English