Here is what the tips & notes say:
"The mainly South Wales variant is formed by adding the appropriate ending to the stem of a verb.
"The mainly North Wales variant is formed by using the verb Gwneud (to do/make) as an auxilliary verb. This is analogous to the English 'I did'"
They appear to be different ways of saying the same thing.
Not really. Apart from some common verbs (dod, mynd, cael for example) the use of bod or gwneud as an auxiliary to make compounds verbs very common in the spoken language in all dialects. I think the course mentions another way of constructing the simple past, too - by using daru/ddaru - that is common in the north-west in particular:
Mi ddaru i chi brynu bara - 'you bought some bread'
Fe wnaethoch chi brynu bara
Buoch chi'n prynu bara
Rydych chi wedi prynu bara