The diatonic scale, in the key of G, "starts" with GAB - not all songs in the key of G start with these 3 notes

A major scale (any major scale, whatever the key) obeys the simple rule - 2-2-1-2-2-2-1, or - W-W-H-W-W-W-H or T-T-S-T-T-T-S which are all different ways of saying exactly the same thing - and that "thing" is - for the Ionian ( thats major) mode - to get to the next step in the scale you move

2 semi-tones, then 2 semi-tones, then 1 semi-tone, then 2, then 2, then 2, then 1

OR

a Whole step, then a Whole step, then a Half-step, then W, then W, then W, then H

OR

a Tone, then a Tone, then a Semi-tone, then a T,then a T, then a T, then a S

The 7 (or 8 if you include the octave) note diatonic scale is a subset of the 12 note chromatic scale, and WHEREVER you start, to create a major scale, you MUST follow the 2,2,1,2,2,2,1 pattern (or either of the two others, same thing)

But - you can ALSO build a scale whose home note or tonic starts at a different "scale degree" - but still obeying the pattern (looping back on itself when you reach the end).  ( I always think in terms of the 2,2,1,2,2,2,1 pattern - it matters not which option you prefer).

So, the G major scale, MUST obey the rule - and that rule picks out the notes G,A,B,C,D,E,F# from the underlying chromatic scale ( i.e. 2 semitones from G to A, 2 to B, 1 to C, 2 to D, 2 to E, 2 to F# and finally 1 to the next G - an octave up from where you started)

If however, you use the notes in the scale of G major, but start at scale-degree 7, you'll start your scale on the E.  But this time (because in THIS case you are using the notes belonging to the pattern of G major), your steps will, from the E, be 2 to F#, 1 to G, 2 to A, 2 to B, 1 to C, 2 to D and 2 to get back the the next octave-up E

This is E minor.  It is one of the 7 "modes" in the scale of G. 

There being 7 notes in the diatonic scale, it comes as no surprise that there are 7 modes.  They all have names.  The "major" scale is Ionian mode, the "minor" scale is Aeolian mode.  Another very common mode is Dorian mode, which starts on scale degree 2.

I'm sure, in some publications, the theory can be difficult to grasp, possibly because of all sorts of different approaches, or incompletely specified fundamentals, or "assumed knowledge" - but it's not really that difficult.  You can soon figure out how scales and modes work at a piano keyboard ( even a virtual one, and there are a number of those to be found on the internet )

The piano - real or virtual - will clearly show how the 2,2,1,2,2,2,1 sequence works - and why some notes HAVE to be flattened or sharpened to make a major scale.

MrYikes said
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But should a miner's minor be playing a major minor or should he just play a minor minor? 

D'Oh !  LOL !   And aye on the 3,1,3,1 (especially if with your moveable "do" you hear / think the solfa name instead of C,E,G or whatever- works, whatever the key.)

Interestingly, my earliest exposure to music (primary school) just used the simple (not the full blown solfege) sol-fa - and - as much as my theoretical understanding has evolved over the years - I sometime catch myself - say playing Ashokan Farewell starting off (in my head) sol, ti, do.... lolol !  Aye, old dog, new tricks, and the teaching thereof !