In the first Terminator movie, the terminators do not all have the same face. They show some enter a building in the future where some humans are hiding out. They look different from Arnie's terminator. I seem to recall it being said in a later film in the franchise that the cyborgs all look the same. Reese said that Arnie's terminator was so advanced, he couldn't distinguish it from a human. Hence, Reese waited.

I realize this might not have answered your question; I'm sorry if it didn't.

@glomps and nibbles said:

This is the exact question i got with Terminator 2 as well T-800 waiting for T-1000 to reach John first

We wouldn't have the twist in the movie unless it was like this.

You know its a good point. Reese isn't even sure he can stop the terminator. Perhaps he was waiting for a good chance to kidnap her and it didn't happen. He was hardly gonna tell her "I was gonna bung you in the boot of me car, but I missed my chance".

@tmdb27030640 said:

This is the exact question i got with Terminator 2 as well T-800 waiting for T-1000 to reach John first

Yeah both Terminators arrive at night in T2 yet wait till the next day to visit John!

Satch said it best...plus Reese likely anticipated Skynet would've anticipated a "common" T-800 skin being spotted, maybe he was a new skin face? I know future Terminator movies changed all that and when you think T-800 you think "Arnie", but I don't think James Cameron was thinking that far quite yet...he just wanted to be able to finish the movie!

After re-watching this recently, @Satch_the_man explained it correctly. Reese specifically said he did not know what the terminator looked like until he made his move. Coupled with the flashback (flash forward?) scene where the terminator infiltrates the resistance base and its clearly not Arnie, it's safe to presume that Cameron likely wrote that they had different 'skin'.

One can assume Skynet made different Skin models of the T-800.

The original actor cast for the T-800 was Lance Henriksen, because it was thought that he'd be able to blend into a crowd. Makes for a very frightening, horror-type killer that is completely unstoppable, and you can't tell who it's going to be. After Lance was bumped over to a bit part as a cop and Arnold was cast as the T-800 (to make the cyborg look bigger and more fearsome), subsequent installments retconned the terminators to have the same face, for the very meta reason that the franchise was more or less a vehicle for Arnie, and they needed a reason to keep him in the movie. T2 may not have been made, I think, if it wasn't treated as an Arnie vehicle. For better or worse.