Maybe. I think the difference is thrillers may scare you, but that is not their purpose. Their purpose is to tell a story and maybe there are elements that scare you. Like MG was talking about, because they scare the character. When I watch a horror movie, and this is the reason I don't like them, I feel like there purpose is to only scare. They have no interest in actual storytelling, any of that is just a device to get to the next jump scare and kill. Nightmare On Elm Street, Friday The 13th, Scream, most Saw movies, Texas Chainsaw. There is no character development, it is just about the scares. Its fine if that's your thing, I think the same can be said of comedies, just replace scares with laughs. To me that's the difference.
Like I said before, my definitions are not the actual definitions of horror and thriller, but for me it has to do with how much is actually shown on screen vs. how much is left for your imagination to scare you. I don't need to see all the blood and gore. That's not scary. It's just disgusting.