Yes, the ChAdOx is an adenovirus carrier (chimp? to minimize human pre-infection) while Moderna and BioNTech as the parent states involve injection of mRNA (not DNA although there are other vaccines that do that) lipid particles that human cells then generate spike protein to simulate viral infection.

There are still other attenuated virus and other vaccines under development, they just haven't reached Phase III. Novavax even does something similar to what you describe (spike proteins with adjuvant), but it's also not past Phase I/II.