Both the Oxford-AstraZeneca vaccine and Sputnik are using a pretty similar trick that gives them the speed-up. They still get to pick an arbitrary sequence, but they're smuggling it inside a virus instead of as mRNA.

That's why the codename for the AstraZeneca vaccine is ChAdOx1, it's a Chimp Adenovirus as host for the sequence. Take this mild uninteresting chimpanzee virus, but tweak it to tell human cells to produce your arbitrary sequence instead of itself. The humans become immune to whatever your sequence was (and maybe to Chimp Adenoviruses?).

I'm sure there are reasons this might be better in some cases, and it involved less bleeding edge technology which made it a safer bet in a pandemic, but the mRNA approach seems obviously more general and even perhaps more re-usable.