It's W-H-W-H.... or H-W-H-W...., so maybe think of it in terms of intervals instead:
Whole-tone first: 1 w 2 h b3 w 4 h b5 w #5 h 6 w 7 h 1
Half-tone first: 1 h b2 w b3 h 3 w b5 h 5 w 6 h b7 w 1
Formally there's probably a better way to write the half-tone first version by calling 3 a diminished 4 or by calling b5 an augmented 4, but hopefully you get the picture even if there's no 4 in the half-tone first version above.
First, notice that each of these patterns contain the dim7 chord (= 1 b3 b5 6). So how do you give the two versions different names? Well, pick which note you want to be the 1 and then see if the next tone is a half-step away or a whole-step away. (I forget what Pebber calls the two varieties, but this should be easy to find in his videos though. Heck, I might even use the names Pebber uses in what follows.)
I gather from your post that your pattern has F# and G in it.
If you want the F# to be the 1, then you're using the half-tone first version because G comes next. Because that version has 1 3 5 and b7 in it, I think some people would call that the F# dominant-8 tone scale (since dom7 or just 7 = 1 3 5 b7).
If you want the G to be the 1, then you're using the whole-tone first version because you came from F#. Because that version doesn't have the b7, I think some people would just call that the G diminished-8 tone scale and leave it at that.
Now if you're itching to give either of these even more names, you can. The pattern of W-H or H-W repeats every three semi-tones, so just change which tone you call the 1. The F# dominant-8 tone scale will have the same 8 notes as the A, C, and Eb dominant-8 tone scales. And the G diminished-8 tone scale will have the same 8 notes as the Bb, Db, and E diminished-8 tone scales.
Anyway, forget trying to fit these "in" a natural minor scale though. You can't fit 8 tones in a 7 tone scale. How about the reverse? Nope. In neither of these 8-tone scales do you have all of the tones you need for the natural minor scale ( 1 2 b3 4 5 b6 b7 ). You either have the b3 and b6 (#5) or the b3 and b7, but not all 3.
Hope this helps.
(Ok, see you all next quarter...)