A mystery: 2

In a proper name that includes a numerical designation, when do we (or most of us) pronounce the name as a cardinal and when do we use an ordinal? For instance, we read Elizabeth II as “Elizabeth the second” but Super Bowl II as “Super Bowl two.” Is the distinction just people vs. everything else? Don’t names of ships sometimes use ordinals and sometimes cardinals? How about horses, like Canonero II?

(Prompted by a momentary misreading of Discoverer I as “Discoverer the first” [Only Revolutions, p. 291S.] Conversely, our friend David refers to Shakepeare’s best-known history play as “Henry five.”)