This looks to me like Cornus nuttallii, our native flowering dogwood. It's a tree.

Looks more like Cornus florida to me. Or maybe one of the Rutgers hybrids.

How would one distinguish between C. nuttallii and C. florida, aside from tree size and shape? And C. kousa while we're at it, aside from bloom time? I learned last spring from bboy how to distinguish between the native hazelnut and the European filbert and discovered that my neighborhood is full of naturalized filberts mixed in with hazelnuts. I'm hoping there's good diagnostic characteristics to distinguish between the dogwoods too.

C. kousa produces pointed floral bracts ("petals") with a straight-sided taper. C. florida bears 4 bracts with notched tips. The bracts of C. nuttallii are 4-6 in number and curving to a point or blunt on the end. Hybrids may display intermediate characters.

Here is a link that might be useful: RUTGERS UNIVERSITY ORNAMENTAL DOGWOODS

How about leaf or twig characteristics? In my line of work I often need to decide if something's native, naturalized or a relict ornamental, when they're not in bloom. With dogwoods I have pretty much been going on location and tree shape to make an educated guess.