It is correct that there is a different pronunciation of the r at the end of a word than an r at other parts of a word. The normal Turkish r is a "tap" where the tongue taps against the top of the mouth, unlike in the English r.
The word-final r that sounds like "sh" is, in technical terms, a voiceless alveolar non-sibilant fricative. It is actually more similar to the English r, but the main difference is that it is not voiced, which means your vocal chords are not vibrating as you pronounce it.
For more information and some sound recordings of the different pronunciations of "r" in Turkish, see the alphabet and pronunciation page on TurkishTextbook.com