A group that is defined as the most living common ancestor of all living members of a group, and all of that ancestor’s descendants, is a crown group. So the most recent common ancestor of all modern birds, plus all of that ancestor’s descendants, is crown birds. This includes extinct things, but they’re closely related to living birds.
A group defined as a living group (such as birds) and all creatures more closely related to that group than to any other group, is called the total or pan group. So all animals more closely related to birds than to any other animal are pan birds.
The group of creatures that aren’t in the crown group but are in the pan group are the stem group. So all animals more closely related to birds than to anything else, but aren’t descended from the most recent common ancestor of living birds, are stem birds.
So, “traditional” dinosaurs are stem birds. You can call them birds, if you want. “Birds” is a more accurate name for them than any other at the end of the day. They aren’t crocodiles, because they aren’t in pan-crocodiles. They aren’t lizards, because they aren’t in pan-lizards. They are reptiles, but birds are reptiles too (the group that includes all things that we call reptiles also includes birds because birds are descended from that most recent common ancestor too). Birds is the most specific name for dinosaurs.
And we call pan-crocodiles crocodiles. Like, we have a real trend of calling all members of the pan-crocodile group crocodiles. And stem-crocs got really, really freaking weird. So there is a precedent for it.
So: non-avian dinosaurs are in a group that has birds in the name. Birds is the most specific name we can give them.
All birds are dinosaurs.
Are all dinosaurs birds?
note: this is a philosophical discussion. at the end of the day non-avian dinosaurs are stem-birds and pan-birds but they aren’t crown-birds. But most of them if you saw them in the street you probably wouldn’t call them a bird (only the ones really close to birds, like Velociraptor, would probably get called a bird). But traits we ascribe to birdhood - beaks, feathers, warm-bloodedness, flight, etc. - all appear in, or are even universal within, dinosaurs.
For more about this silliness check my “#bird political spectrum” tag.