Difference between maximizer and limiter for more loudness?

In mastering, what’s the difference between raising the “optimize” knob on the maximizer plugin versus raising the “input” knob on the limiter plugin, assuming both are set at an equal “output” level (i.e 0db)?

Well, as their names state, the maximizer will increase sound levels up to 0dB (in your example), while the limiter will merely (and gracefully) prevent any sound to exceed 0dB.

But as my original post states, I’m asking someone to compare the difference between raising the “optimize” knob on the maximizer and “input” knob on the limiter to give loudness, if there is a difference. Both plugins prevent the volume from exceeding their “output” level, and both can be used for loudness. Again, how does their loudness (optimize vs input) functionality compare?

They technically are pretty much identical except they are optimized to acheive slightly different aims. A maximiser is tuned to allow the input gain to be pushed way beyond 0db without distorting (too much) or in a way that’s (apparently) musical. A limiter looks to limit the signal as transparently as possible but will distort when pushed too hard, both tools can be used to the same effect - if you’re gentle with the input gain. Limiters were often called clippers because they (well, some) effectively top and tailed the over driven waveforms to control peaks, but modern processing power means modern limiters tend to act as aggressive compressors, keeping the shape of the loud waveforms, just turning the quiet bits up.