The AZ one isn't a direct mRNA one, but it's a modified adenovirus that can't fully reproduce itself but can infect cells and hijack part of them to mass produce copies of just the covid outer spike protein that the antibodies react to. Neither of them should strictly be DNA altering, generally things go DNA>RNA>protein and not back up the chain, but biology's stupidly complex and everything gets messy if you look closely enough, so never say never I guess.

They're both newer forms of vaccine than the usual attenuated/inactivated viral ones you will probably have had in the past, so there's a murky water either way, but at least some other adenoviral vaccines were further along in trials than any mRNA ones were when covid started.

And you've probably seen a lot about it here because TheImpossible1 didn't like the lead woman (guess why) involved with the vaccine development and was shorting AZ stock heavily and trying to wish the failure of the AZ vaccine into reality to help that. Plus the EU is still busy being petty about the UK and their exports, and the pre-emptive bans of only the AZ vaccine by EU countries (despite coincidental side effect rates similar to the bell's palsy rate seen in the mRNA vaccines) were well placed to generate dramatic headlines and damage confidence in it, so make of that what you will.