Why are these so similar if their algorithms are so different? (amod vs fmod)

I find that these sound similar except that, at low frequencies, the second sounds twice as fast as the
first; but I was expecting the second to involve an audible vibrato-type effect instead of an amplitude
effect:

play "|sox -n -p synth 0 sin 440 vol .4" synth 60 sin am 1-500
play "|sox -n -p synth 0 sin 440 vol .4" synth 60 sin fm 1-500
                                                      ^^

I suspect I misunderstand the nature of fmod here. I thought the amplitude of the second wave would alter
the frequency of the first.

I was finally brought to ask this when studying today the similarity between synth amod and
--combine=multiply, because I was looking for something that would let an input adjust frequency instead of
amplitude.

-- 
Doug Lee                 [email protected]                http://www.dlee.org
Don't be afraid your life will end; be afraid that itwill never begin.
-- Grace Hansen