Yes, this is how it worked for us and our oldest son (who is now 24). His classification for the purpose of early intervention through the school was "developmental delay." His medical diagnosis was spastic quadriplegia (cerebral palsy). When he hit about 1st grade, for school purposes they had to change his classification - they went with "other health impaired" because he's nonverbal, visually impaired, as well as quad.
The reasoning for this (according to our school at the time) was that a lot of times kids with developmental delays catch up during those early intervention years, so that by the time they hit 1st grade there's minimal, if any, delay. They use "developmental delay" as a catch all in those early years. For the kids who still have a delay, a more specific classification is needed (I believe has to do with funding issues for the schools). For example, my son's disability is so severe that it's considered "low incidence" and his SDs always got more funding to educate him - hence the other health impairment classification.
In terms of a medical diagnosis, I don't believe you should take the school's determination as fact. They're not doctors and are solely concerned with the educational impact of his delays. Has he been evaluated by a developmental pediatrician or a neurologist or... some other MD?
You can ask the school what specific tests are going to be performed. I would guess there will be gross motor/fine motor/cognitive/etc tests. Again, they're just going to be looking for his strengths and weaknesses, and what areas are going to need to be covered by his IEP.