Edit: Sorry, missed this one:
According to Ed Solomon, one of the creators of the franchise, the babies at the end of Bogus Journey are indeed the same daughters in Face the Music. There's a line in the 3rd movie where
spoilers:
Ted's father regrets going along with calling the girls Lil Bill and Lil Ted because while everyone thought it was a cute idea, it only started the kids on the path to emulating their dads. |
end of spoilers
IRL in the second movie, the babies really were intended to be sons, but the casting department cast two baby girls (which is still common practice in TV/Film -- who would ever know?). Solomon learned of this behind-the-scenes fact and decided to run with the idea when he first started working on the script in the mid-2000s, especially since there are old female counterparts to the names Bill & Ted (Wilhelmina and Theodora, and hence Billie and Thea).
Yeah, Bill and Ted had great knowledge of rock music in the first two films but the daughters have extensive knowledge of music, music history, and music theory,
spoilers:
which is what enabled them to assemble the supergroup in the first place. Plus, at the very least they knew how to pronounce those figures' names in contrast to the running joke of the first movie of Bill and Ted constantly mispronouncing historical names (So-Crates). And then, of course, the prophecy ended up being that the daughters were the ones all along who would write the song that would repair all of space and time while their dads (The Great Ones) bring it all together -- Bill and Ted were smart enough to know that they weren't actually smart enough to write the song, but in the same amount of time they spent looking for that song was the amount of time (roughly) it took the girls to assemble the band and make the song. Plus, they accomplished their time travel mission faster and more directly than Bill and Ted did in the first movie, and Billie even kept Bill and Ted focused when dealing with Death in Hell. |
end of spoilers
Maybe the sweetest example though was at the beginning at the wedding -- the girls were the only ones who knew what Bill and Ted (who are now great and experienced musicians themselves, even if washed up) were going for with that ... unique... piece. It may have sounded terrible, but the girls appreciated what was going on and were digging it.
But it's also strongly implied that a lot of that is from their upbringing, and so saving the universe was a family effort.
And if you haven't seen the original movies, I'd strongly urge to. They're officially free on YouTube (not pirated) and they're very sweet and whimsical, but you'd get a better picture of Bill and Ted's problem solving skills compared to their daughters. The dads have a much harder time making the simplest connections, but they still try their best and it's endearing...and surprisingly effective.