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I consider all three terms interchangeable, though they all have different connotations, and square in particular has two ways it can be used.
1. "pulse" suggests that the duty cycle is short compared to the period, or at least that it may be a length unrelated to the period (i.e. there is a potential asymmetry).
2. "square" suggests that the edges of the waveform are square. Some people will use square to specifically refer to 50% duty to distinguish it from the other words, which is is taking square to also mean "symmetrical". The more exclusive use for only 50% duty waves is not universal; it is still quite acceptable to talk of a 25% square wave as long as you are consistent about it in that context.
3. "rectangle" is a less common term for a waveform, but it is used for the same reason as square (i.e. the edges of the waveform are like the corners of a rectangle). This tends to be used by people who use "square" as only 50%.
Even the use of the word "duty cycle" is rather strange when applied to audio. Duty cycle is taken from descriptions of power generators or control signals that are on part of the time in a periodic way, meaning any work done that is controlled by this signal has a cycle of duty. When applied to audio, this is a bit weird because the signals are not really power signals, and will be mixed together to control a speaker, but not in an on-off process like in the original meaning of "duty cycle". Also, since all sound produced by the speaker is differential to the signal, the output itself is once removed from the idea of a duty cycle. (Maybe something like a PWM DAC can be considered to have a proper duty cycle.)
So... as far as the NES goes, "pulse" has all the right connotations. The term "square" has some ambiguity because a lot of the time it's appropriate to use it exclusively for the 50% wave. I would avoid "rectangle", personally.
I call them "pulses" if they're asymmetrical, "squares" if they're at 50%, and "hot transsexual porn" only applies to PWM.
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