One vaccine doesn't even trigger the same immune response in different people, so it is not entirely clear to me what you mean.
The basic principle of a vaccine is that it contains proteins that are the same as (or similar to) some of the protein building blocks of the actual virus. Your body learns an immune response to these proteins, which it can reactivate when it encounters the real thing.
Many potential vaccines target the same spike proteins on the outside of the virus. I guess you could say those produce "the same immune response" in that sense.
Not the "same", but according to a Nature review on vaccines from last month, most vaccines exhibit a very strong immune response (usually, for the two-dose regimen, after the second shot).
The nature of the response varies. Some candidates are more efficient at eliciting the production of antibodies, while others also activate cellular immunity (T cells).
No. AFAIK, they may target different proteins on the virus hull and also differ in other respects among each other. Some of them might be less effective than others, some might be more prone to being rendered ineffective by virus mutations than others, there can be substantial differences in the number of complications caused by vaccination, and some of them could also cause problems with developing future vaccines for deadly coronavirus variants that may occur another time.
At least, that's how I understand it from what I've heard. Others should please correct me if I'm wrong.
