Ah, I remember also answering a question like this one on Electronics Stack a while back.
In stead of looking it up and linking it, I shall just type a new answer, in the hope my sleep deprived brain will say it right and understandably.
The square wave is a sneaky one. Actually any wave that isn't a Sine Wave is sneaky, but they are all sneaky in different orders.
In spectrum speak a squarewave of 2MHz is basically applying a figure of speech, where you actually mean to say "A square wave with a dominant frequency of 2MHz" or "A square wave with a base frequency of 2MHz".
((EDIT: added "in spectrum speak", since a signal that repeats once every 0.5us of any shape is in general engineering speak correctly specified as being 2MHz))
You see, that nice sharp flank that is the edge of the square wave is, on paper, in fact "infinite frequency" (of course, that doesn't exist in the real world and as such nor does the true square wave, they're always a tiny bit not-square).
The funny thing is, that sharp flank implies a set of higher frequencies that we call overtones. Such that when you measure the frequency spectrum of a square wave, you can see 2MHz, but also many frequencies that are a multiple of that frequency, but less powerful.
Because I am not yet aware of nice drawing or simulating tools linked into here, I will link to the wikipedia animation here:
http://en.wikipedia.org/wiki/File:SquareWave.gifCopied from:
http://en.wikipedia.org/wiki/Square_waveThe first frequency is the base frequency, 2MHz, the next frequency is the next odd overtone: 3 times as much, but 3 times as weak, so 6MHz at 1/3 the power. Then the next one is the next odd overtone, so 5 times as high, but 5 times as weak, so 10MHz at 1/5 the power, the next is the 7th, 9th, etc, etc, until some part of the circuitry can't process the overtones anymore and they start cutting out.
From your experiment, the generator apparently has a part of its circuitry cut off somewhere between 20MHz and its 3rd tone, 60Mhz, which is quite normal for analogue generators set at their maximum frequency. So you are only getting the base frequency with maybe some distortion and shift caused by the overtones in stages that actually can handle them, which is just the one sine wave.
EDIT2: See, I said it sort of wrong, I said Overtone, where more correctly it should be Harmonic. Insomnia, it's not fun.