To be more precise, everything now links to an MDX profile.
A MagicBand or your "admission card" is they key to the profile. Note that Disney no longer calls it a ticket - it's an "admission card", and serves the same function as a MagicBand for most purposes. The admission card may be purchased with a ticket entitlement "on" it, but when you register it, it places the ticket entitlement in your profile, and links the admission card ID to the profile as well.
Also part of your profile are resort reservations, dining reservations (ADRs), and Fastpass+ reservations. By registering a resort reservation, that _might_ enable other features, like the +10 ability on making dining reservations, and also the rumored +10 ability on FP+ reservations, within the window of the reservation.
When making FP+ reservations, it looks to your profile for eligibility, which in general (as we currently know it) is that you have a valid ticket entitlement active in your profile, with the appropriate number of days available and within the allowed range for that class of ticket (60 days for MYW and AP, unknown for others), and that you are eligible (an arbitrary flag controlled by Disney). It does not necessarily look to your reservation, except potentially for that +10 benefit...it doesn't know if the ticket you have active is the one that will be used for that reservation or perhaps an off-site stay or day trip. (Package tickets may be handled a bit differently, but I doubt it, since many people get packages and keep the tickets for later use)
For day trippers, or those that buy tickets but never establish an MDX profile, my assumption is that on entry it creates an "anonymous" profile, which allows admission and perhaps day-of FP+ use and limited kiosk use for arranging FP+ that day and maybe the next X days, but there would be no app or web access.