Duplo are the bigger ones for younger kids.
Mega Bloks is the cheaper one. Ask me, I’ve bought them all. Legos, Mega Bloks, Flexi blocks. Those were the days. :)
Ours were made by Tyco, as I recall, and it seems like they had some sort of other name rather than Mega Bloks, but you could be right! They were mostly compatible, but the bumps were a little shorter, so sometimes they didn’t grip as well. The real ones tended to get used first.
And yeah, now I remember the Duplos! I think we had a set or two of those mixed into the rest...