Story behind rz is a bit different. In Polish we have letter "z-with-dot" which sound similar to french 'j' (like in "je" or "jalousie"). Way r is pronounced is Polish is close to "z-with-dot" tongue-wise (r is front of palate, z-with-dot is middle of palate, vibrating in both cases, even if slightly differently).
In old Polish, a lot of words had "r" in some places, which, due to language evolution (and probably people getting lazy, as rolling r is harder to say than "z-with-dot") slowly converted into z-with-dot. But in meantime, they were something in between r and "z-with-dot" and "rz" was used to signify that. These days, it should be just "z-with-dot", but it is a spelling mistake, because you know, poets from 150 years ago and old people.
For normal Pole, "rz" and "z-with-dot" is pronounced exactly the same. Same for "u" and "o-with-accent", and "h" and "ch". Some people will claim there is a small difference, but they are mostly snobs - more than 95% of people won't know the difference.
Useful ones are "cz", "dz", "dz-with-dot", "dz-with-accent", "sz", they really indicate separate sounds.
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