I would think that the transition duration between slides would be a part of both slides' time duration and not add or take away total time of the slide project.
That's totally correct. The transition duration is a part of both slides' time duration, so it's not an additional value. You can clearly see it if you switch from Storyboard to Timeline.
when I change the duration of the transition between two slides it messes up the timing of the slides with the synced music going forward. Am I missing something?
The point is that during the transition, both slides are on the screen simultaneously. You can see the previous slide disappearing and the next slide appearing - both of these happening at the same time. So, for two slides, if the duration of each slide is 7 sec. and the transition duration is 2 sec., the total is 7+7-2 = 12 sec. In other words, for the first 5 seconds, slide 1 is on the screen on its own, then there are 2 seconds when it is being wiped off / dissolved etc. and slide 2 starts to appear, and for the next 5 seconds, slide 2 is on the screen. I hope you get it now.
So, if you change the duration of some transitions, the total slideshow duration will change inevitably. For example, if you make transitions longer, the whole slideshow will become shorter.
what's the difference between a constant speed transition and a smooth transition?
It's about animation modes actually. In smooth mode, there is some acceleration at the start, then constant speed, and the object slows down towards the end - it's all to prevent jerkiness.