“Kinematic”/“static”/“dynamic” are common terms in various physics engines.
I doubt that you can get the “exact” behaviour that you are looking for, since the kinematic body is deliberately bending the rules of the dynamics solving. For instance, your kinematic body has infinite mass, which the dynamic bodies doesn’t. You can set the position, which gives you the opportunity to put your body in the middle of a bunch of dynamic objects, which (usually) doesn’t happen for dynamic objects. And, your body doesn’t respond to forces. And finally, updating the kinetic object happens after the solving step, not during it. All in all, I think it’s very difficult to make them behave exactly the same. Personally, I’d go for “similar, under certain conditions” 
EDIT:
Here are some links to bullet and Box2D (search for “bodies”) as a starting point.