“Consecutive” means one after another. So like if it’s a rare day where I’m winning on Overwatch, I might say I’ve won three consecutive matches, if I won them without any losses in between. If I had a loss in the middle, I could say I won three non-consecutive games.

“Continuous” means without a gap. So it’s similar, but it refers to one ongoing thing rather than several things happening one after another. In the above example, my match wouldn’t be continuous, because I played three separate matches, but my winning streak would be. Or if you never turn your tv off, it’s on continuously (as an adverb describing it being on). The opposite would be “intermittent” - sometimes on, sometimes off.