I’ve seen a lot of other people on my dash already answer this question probably a lot better than I can, but here goes nothing anyway.
I’d love to see their relationship slowly grow into more as the result of a basic sort of trust between them developing and solidifying. They keep taking turns saving each other’s asses, and as a natural progression of that they would start to lean on one another in other regards as well. They’d start to depend on each other more and more, not just as an ally in a fight, but as an ally in all other parts of their lives as well.
And eventually a closeness would develop between them that I don’t think either would even notice until they were fully immersed in it. It would sneak up on both of them and one day they’d find themselves actually opening up to the other and they’d have that moment of realization where they suddenly understand “oh shit, I actually care about this guy.”
I think the more overtly romantic/intimate side of their relationship would have a similar slow-building onset. Accidental touches that start to linger, meaningful stares that both would deny mean anything. They wouldn’t necessarily even admit to themselves that this is starting to become something. And they probably still wouldn’t until something finally forced it out of them. Everything would come to a head during a heated argument, or during another life-or-death situation, because the threat of death is probably the only thing that would get either one of them to snap out of it, man up and go for it.
This is going to sound completely out of left field, but I picture it almost like when Josh and Donna on “The West Wing” finally got together. How the only thing that finally pushed them over that edge into this new stage of their relationship was that they were so wrapped up in the moment of their excitement that they kissed without realizing what they were doing until it was already done.
I can easily imagine something similar happening between Derek and Stiles. Especially with how Stiles just throws himself into things. The way he expresses his upset and then subsequent relief over Derek’s near-death in episode 1x04 “Magic Bullet” is so enthusiastic and head-first, and they didn’t even know or like each other at that point. So imagine his reaction to a similar situation if he actually really cared about Derek. He’d practically tackle the guy without even thinking. Without even having time to be embarrassed or to realize what it means until after the fact.
And then later, as their relationship continues growing, I don’t think their core dynamic would change that much. They’d still be Derek and Stiles, they’d still butt heads occasionally and snark at each other and challenge each other in ways that are as frustrating as they are necessary. Just, you know, with bonus making out. And also, more importantly, with a more obvious and deeper element of trust between them that would bind them together and make them both stronger, no matter what else gets thrown at them down the road.