Difference : Lt spice AC analysis and frequency analysis in time domain
As far as I can tell, what SPICE calls "AC analysis" is exactly what you described as "frequency response analysis".

But if you're specifically asking about switch mode supplies (which you used in your tags but never mentioned in your question text) the difficulty is that they aren't operated at a quiescent operating point with AC variation around that. A switch mode supply generates its output based on time averaging of a dynamically varying signal to produce a more-or-less steady output. Traditional SPICE AC analysis isn't able to simulate the time averaged response of this kind of system.