Hey /sci/

So I've been reading Do Carmo's book on Differential Geometry and I'm struggling to understand why he defines "regular curves " and "regular surfaces" so differently.
He defines a regular curve as a smooth one parameter function such that its derivative is never 0. He defines it to be simple if it also doesn't self intersect. Now he defines a regular surface as a smooth two parameter function, such that its jacobian is rank 2 (analogous to not having a zero on its derivative for curves) and it is locally homeomorphic to the plane. This last thing basically means that self intersections are not allowed on regular surfaces. Now that was the idea for a simple curve, so as far as I understand it's okay for a regular curve to self intersect (for example a lemniscate is a regular curve), then why is it not okay for a regular surface to self intersect? Isn't there a notion of a simple surface?