There are three types of dogwoods that I am aware of that can have white berries - Red Osier, Rough Leaf and Grey. All of them can have somewhat of a red cast to the stems, but as a general rule, the RO has the most and Grey has the least. Rough Leaf can have a hairy appearance on young stems and leaves. The best way to tell them apart is the blooms which are somewhat different.
I'm going to say that one is Red Osier.
That second shrub is bush honeysuckle. Look at this link.
http://www.oardc.ohio-state.edu/weedguide/single_weed.php?id=54
Edit - just noticed you said the stems were not hollow. Hmmmm, sure looks like BH. Did you snap one on a larger limb?
If not Bush Honeysuckle - look up Coralberry and Fly Honeysuckle. Both are look alikes but I don't have either growing here and don't know them very well.
Good luck..........