What do 'product' do? The actual design, which is then handed over to engineering for implementation?
Something like that, yes.
There's Product Managers, Project Managers, Program Managers, Engineering managers.
I think what happens is you have Product guys on one hand and Developers on the other.
Engineering is inbetween and consists of the calculus of tradeoffs both from the technology and from functionality. Most of the people with "engineer" in their title are really developers, that just implement.
Then again, all this Silicon Valley software company mumbo jumbo is new to me -- I'm still somewhat new to this industry...
Suffice it for now that the separation between product and engineering makes neither better.