I guess I could check out the SEP articles related to this topic, but I'll ask my question here for... I don't know... Let's say "educational purposes."

Now this is the entire thing: do logicians differentiate between, "X has happened most/all observed instances of Y in the past, so X will happen the NEXT time Y happens, too," and, "X has happened most/all observed instances of Y in the past, so X will happen ALL times Y happens in the future, too"? Would there be any significant reason to differentiate between these two types of inductive conclusion?

Generally speaking logicians prefer the former of the two you mention. Induction takes us from empirical premises to empirical conclusions supported by the premises, but not deductively entailed by them. Thus, inductive arguments allow us to infer probable conclusions beyond the content of the premises. For a fuller explanation I recommend Graham Priest's Logic: A Very Short Introduction.

Hope this helps.

Szavieur wrote:
I guess I could check out the SEP articles related to this topic, but I'll ask my question here for... I don't know... Let's say "educational purposes."

Now this is the entire thing: do logicians differentiate between, "X has happened most/all observed instances of Y in the past, so X will happen the NEXT time Y happens, too," and, "X has happened most/all observed instances of Y in the past, so X will happen ALL times Y happens in the future, too"? Would there be any significant reason to differentiate between these two types of inductive conclusion?

That's not really different types, it's just
a question of statistical confidence.
You can have almost no confidence it will
happen every time hanceforth, and vastly more
confidence it will happen once (next).