Apple Invites you to use Invites, a new invitation app that lets you invite people with Invites
Apple's latest app is designed to make custom invitations for family and friends digitally, though you'll need an iCloud+ subscription to create invitations.

I think I like the idea of Apple's new Invites app.
It's designed to make events more memorable and sharable. It's a free download on iOS, but if you actually want to use it to send people invites, you need to be an iCloud+ customer, which costs a minimum of $1.49/month. So it's not really free.
Receiving invites and RSVPing don't actually require an iCloud account, fortunately.