The AdGuard app is a full-featured ad blocker that works across your entire device, blocking ads in apps (DNS) and Safari (content blocking), with more control and customisation.
AdGuard DNS is a simpler, DNS-based service that blocks ads by preventing connections to ad servers, but it's less customisable and doesn't block ads as deeply within apps or websites.
App: More powerful, customisable, works across all apps (for DNS) and Safari.
DNS: Simpler, lighter, blocks ads on a basic level by changing DNS settings.