Clarification

And tons of death metal is really fast...

Of course death metal can be as fast, but it's not the same kind of constant driving jolt of energy you usually get in thrash. Death metal is generally a bit more structurally complex, with emphasis also placed on dirgy, brooding passages at least some of the time.

Not to sound condescending (since I may have wondered about this stuff myself at some point), but the answers to these questions will probably become more clear just from listening to the music more, not from any verbal explanation.
 
Most of the time, thrash is defined by the style of riffing which is pretty fucking fast with a constant driving rhythm.

Thrash riffing is less a contast up/down picking and more groove oriented. Of course bands like Unleashed have that grove....but then there's the matter of Unleashed's blast beats and vocals. The difference though can even be found in the production, you'll rarely fine the amount of bass on Immolation's albums on a thrash album.
 
I always thought of Death as generally being a lot lower in sound & vocals than any Thrash was. It's still a kind of blurry line to me when differentiating certain old school Thrash from old school Death bands. There are obviously Thrash bands that have that signiature sound, but the line gets hazy with those older Death bands... For example to my ears Massacra's "Final Holocaust" sounds like about the most brutal trill filled Thrash out there, but I would have a hard time calling it death with a straight face. M-A says it Technical Deach Metal, I think... Old Obituary falls roughly into the same category. Old Morbid Angel is a hybrid of the styles.

That's about the way I percieve it, I dunno. There are obviously bands that are clearly one or the other however.