If you don't know what SMS app you are using it will just be whatever app the manufacturer pre-installed (which is different on different phones).
Group messages might differ because there are 2 types of group message: they can be sent as MMS or SMS (though many apps describe the difference less clearly). If the group chat is sending as MMS that might be different from when you text the person individually as SMS.
I think the difference between MMS and SMS group chats is that as SMS each person receives their own copy, so it doesn't actually work as a group chat. This means it's quite likely that you are using MMS. I've no experience of this because here in the UK SMS have been effectively free for most people for more than a decade while MMS are charged per message (and quite costly), so nobody I know uses MMS for group chats. The fact that iMessage only works properly on iPhones (reverting to SMS/MMS for others, sometimes problematically) and RCS (the "Chat" feature in Google's Messages app) only works on Android means that most group chats here are done using cross-platform third-party apps (WhatsApp, Messenger, Signal, Telegraph and the rest).