'Senior people' does not mean elderly. So I'd say of those two, 'elderly people'. Synonyms for 'elderly people' would be: Seniors (Possibly. I can't say I've heard it used for 'elderly people' and, as GuideDogSaint says, it would be heavily reliant on context.) Senior citizens (Possibly UK only, some feel it's patronising.) Old people The old The elderly The aged Pensioners (Off the top of my head.)

Elderly people (or 'the elderly') is fine. Seniors is ok but a little less clear as it can mean important people, final year students and other things. Context should make it clear though.

Although by 'application' I guess you mean the app itself rather than an application (request)? Here it might be better to simply say app as that is what most people say now.

In the US, neither are impolite but they might have different uses. As nouns Seniors make up a large part of our business. (An age category. Seniors might be defined by 65+. A healthy 66 year old would prefer this to “the elderly”) We need to make accommodations for the elderly. (Because their age reduces their capacity. ‘Seniors’ would be ok, though) As an adjective We visited my elderly grandmother. (Not ‘senior’)