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I know that there are many terms that can be used to talk about the tempo of a piece of music but what words are there for change in tempo?
The only ones that I can think of are:
Are these all correct in regards to changes in tempo and are there any others?
They're all correct, though some have meanings beyond just speed. Smorzando means slower AND softer - 'dying away'.
Meno mosso, piu mosso, ritenuto refer to sudden rather than gradual changes in speed. This can cause confusion as both ritenuto (sudden) and ritardando (gradual) are abbreviated to 'rit.' The only clue may be the presence or absence of an extension line. A gradual change has an extent, a sudden one doesn't.
They are indeed tempo change markings, but some of them mean something along with tempo change.
Accelerando means to speed up, to accelerate. That's pretty intuitive.
Rallentando and Ritardando both mean to slow down, but they have slightly different connotations. Rallentando is a sort of fade out type of slowing down, whereas Ritardando is a more deleberate slowing down.
Calando means more than just slowing down. If you want a fadeout to a certain point in both dynamic and tempo, this is a good marking to use. You could mark ritard. and dimin. which would get you a very similar result, but Calando is a way of getting across both a diminuendo and a ritardando without marking ritard. or dimin. Calando literally means to calm down.
Stringendo is another marking that means to accelerate. But more specifically, it means that the music should get more excited. This is often interpreted as Accelerando + Crescendo, because both Accelerando and Crescendo add excitement and/or tension to the music, especially when combined.
Smorzando is another fadeout marking. It literally means dying away. Now, when to use Calando vs. Smorzando? I personally do this:
Rubato is a bit different than all the others because the tempo change isn't unidirectional with Rubato. Rubato means that the tempo is flexible. How flexible it is depends on many factors, like for example Liszt's rubato is more flexible than Chopin's rubato and Beethoven has only the slightest bit of rubato.
There's a particularly common tempo change marking I'm surprised isn't in the OP: allargando. It marks a gradual slowing and broadening of the music. An interesting example is the optional, parenthesized allargando marking near the end of the C major section of Edward Elgar's Pomp and Circumstance March No. 3 in C Minor, which I've heard orchestras inconsistently follow (just like you'd expect).
