Yeah, I agree about the second ship. I had only seen the teaser once before it came out today, and one quick shot of it wasn't enough to identify it properly. Looking at the nacelles alone, it clearly isn't Enterprise.
The ship rising out of the water is definitely Enterprise though. Nacelles are identical and you can at least see NCC-170 on the side. That means more than one ship ends up in water, which is...odd.