The first time they meet Derek never looks at Stiles while talking to Scott. Stiles on the other hand gapes at Derek, fascinated and surprised by his appearance, plus after six to ten years he still remembers who Derek is, and what has happened to his family. Stiles is visibly affected by this meeting. Scott isn´t. Stiles gives the weird impression that he had met Derek before. When he told Scott about Derek´s past the werewolf was still close enough to hear what Stiles said about him. So? Did he?

Is Derek affected by the meeting? Hard to tell. Derek is a mystery. Probably he was listening to Stiles and Scott as they made their way through the woods or else he wouldn't have known Scott searches for his inhaler. So Derek knows that Stiles is theorizing about werewolves and about Laura's murder. Derek is focused on Scott, because Scott is a new complication in his life. Stiles means nothing to him and he should forget about him the moment he's out of sight. Well! Life is a bitch. *snorts*

Derek is dressed in black. Stiles wears a shirt with the image of a target. Oh. That fits.

Scott: "Oh, is this about the body? Did they find out who did it?"
Stiles: "No, they're still questioning people, even Derek Hale."
Scott: "Oh, the guy in the woods that we saw the other day."
Stiles: "Yeah! Yes. But that's not it, okay?"

Stiles is completely keyed up with the research, the possibility of Scott being a werewolf. Stiles has a dismissive attitude when it comes to Derek being a suspect.
Even Derek Hale, he says, like the thought that Derek could be the murderer is kind of ridiculous. He gets pretty excited about Scott remembering Derek. Oh.

When Scott smashes Stiles against a wall Stiles doesn´t make a sound, but when Derek does the same to Stiles in the episode Wolf´s Bane Stiles attacks Derek verbally. Why? What's the difference? Maybe that Scott is his best friend and Derek is a very attractive stranger?

Scott: "No! Listen, you gotta find Allison."
Stiles: "She's fine, all right? I saw her get a ride from the party. She's--she's totally fine, all right?"
Scott: "No, I think I know who it is."
Stiles: "You just let me in. We can try--"
Scott: "It's Derek. Derek Hale is the werewolf. He's the one that bit me. He's the one that killed the girl in the woods."
Stiles: "Scott...Derek's the one who drove Allison from the party."

At first Stiles is convinced that Allison is safe with Derek when he drives her home from the party. Stiles doesn´t think that Derek could be dangerous in any way or possibly responsible for the murders. Maybe because Stiles knew Derek before the Hale fire and spent enough time back then thinking about Derek. Only now when Scott points out that Derek is the one that bit him Stiles believes that Derek is dangerous.

In the woods Derek orders Scott to "Run!" Interesting that he says the same to Stiles in Abomination. So is it a pack thing then? Does that mean Derek considers Stiles to be part of the pack at this later moment?

Well! There is no hate between Stiles and Derek. Just curiosity and confusion.