Theres this thing Metallica does in Shortest Straw and to a lesser extent in Master of Puppets where they take the main riff and shift it up by 2 frets then they have a new section in the original open e position. It gives the song a nice sense of progression and was wondering what its called, my friend said it might be called modulation but he's not sure
Yes, if you shift every note up the same amount you are changing key and that's the same as modulating. The songs you mentioned go from an E scale to a F# scale (two semitones higher). I should listen the songs again to determine if it is minor/phrygian/locrian or another mode but this should answer your question :-)
Yes modulation is when you shift the songs tonal centre to another key. For example, modulating from Em to F#m and structuring your harmony accordingly.
It kind of is and kind of isn't. I would say it's just changing the chord. The riff does have many power chords in it but I would say they don't have a function. The only functioning chords in the "Shortest Straw" riff are E5 and later after the "modulation" F#5. I would just say the song uses E5 - F#5 progression rather than modulation (or E riff - F# riff "progression"). This is really common in Metallica (and other thrash metal) songs. Actually I wouldn't really even talk about chords here. They play an E riff and F# riff. And I would say the song is in E minor all the time. Only the riff before solo part uses real chords (Em-F-D/F#-G). Otherwise it's a more "riff-based" than "chord-based" song and I wouldn't really do a harmonic analysis of it.

But yeah, you could look at it as a short modulation to F#.
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Modulation means you go through a whole form in a different key. I'm not familiar with the tune, but if that's what happens, then yes, it's a modulation.

Modulation has a little brother called Tonicization, where you just establish a different harmony within the key you're in (such as resolving E7 to Am in the key of C).

If they're just moving the riff up or down for one of its repetitions, then I'd call it tonicization (or even just a chord change). If they're moving an entire verse or section of a song, then it's modulation.

Once you get outside of traditional sounding music, it can be kind of a gray area.