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#R, 48 <s>50</s> <s>61</s> bytes
As an unnamed function

 function(s)sd(range(sign(diff(utf8ToInt(s)))))<1
Thanks to @guiseppe for a few extra bytes.

`charToRaw` takes `s` and splits into a raw vector. This is converted to integers and a `diff` applied. `sign` makes the diffs a single unit. `range` reduces the vector to it's minimum and maximum. Then if the standard deviation `sd` is less than 1 it is TRUE

[Try it online!](https://tio.run/##Pck9DoAgDIbh3YtQRjcHPYC7F@CnJSwloeX8FUPiNz353m50GQ1OWhuDeMnQAxcEqYUhVyIYSsfTbtaZv527EThFUee3qRDTQophISP2pY6Y/2/KXg "R – Try It Online")