That's right, tickets and reservations often do not have a 1:1 mapping, particularly when you (1) involve multiple carriers, (2) have many segments, or (3) make changes.

Have a look at IATA Resolution 722f. Off the top of my head, I think there's some tortured accounting that gives you up to 16 flights per e-ticket number. (A direct flight, e.g. SQ61 IAH-DME + SQ61 DME-SIN, counts as a single flight.) This can be expressed as "16 coupons per e-ticket" or something baffling like "4 consecutive tickets, each containing up to 4 coupons, per e-ticket".

So if you want a PNR with >16 flights you'll need two e-ticket numbers. Hooray.

Some UA-related ways you can end up with multiple ticket numbers:

(1) When UA issues award tickets that involve travel on partner carriers, they sometimes create some extra "conjunction tickets" for each separate carrier, sometimes as many as one per extra carrier, meaning that a simple IAD-FRA-CDG trip might have a UA e-ticket number covering UA IAD-FRA and a UA e-ticket number covering LH IAD-FRA. Can usually spot these conjunction tickets because the # is 1 digit higher than the base ticket and because when you look it up you're shown the base ticket number.

(2) If you make a change to your trip after it has begun, the old e-ticket will show some portions "flown" and some portions "refunded"; the new e-ticket will only contain the new segments and will eventually show those "flown". Both the old and new ticket definitely need to be attached to the PNR for accounting purposes but only one is actively in use for travel.

(3) If you make certain kinds of irrops-related changes to your trip, you may get a "single coupon exchange" which results in a brand new e-ticket being issued to cover only one of your segments. I've had a FRA-SIN // SIN-HKG // HKG-FRA flight with 1 e-ticket covering all 3 sectors; after some irrops, UA rebooked SIN-HKG on SQ and I ended up with one e-ticket that just had SIN-HKG on it ("open for use") and another e-ticket that had HKG-FRA on it ("open for use").

To understand this stuff better, become a travel agent (and let me know if you can find an affordable way to become a home-based travel agent / get your own GDS access…)