This language looks like it came from a patent license agreement and is pretty typical.
I think "claim priority from" could be interpreted as a direct priority claim, whereas "claim the benefit of" is a bit broader as it more naturally includes indirect priority claims.
Here's an example of a definition I've used that includes both phrases:
“Patents” shall mean: (i) the patents and patent applications identified on Exhibit A and any and all foreign counterparts of any of the foregoing; (ii) any and all patents that have issued or may issue from any of the patents or patent applications described in (i) of this definition; (iii) any and all patents and patent applications that, in whole or in part, claim priority to (directly or indirectly), or the benefit of the filing date of, any of the patents or patent applications described in (i) or (ii) of this definition, including any and all child, continuation, continuation-in-part, continuing prosecution, divisional, provisional, non-provisional, reissue, reexamination, substitution, extension and counterpart patents and patent applications of any of the patents or patents applications described in (i) or (ii) of this definition; (iv) any and all patents and patent applications from which any of the patents or patent applications described in (i) or (ii) of this definition, in whole or in part, claim the benefit of priority (directly or indirectly) or otherwise claim the benefit of the filing date, including any and all parent patents or patent applications of any of the patents or patent applications described in (i) or (ii) of this definition; and (v) any and all extensions or renewals of any of the patent or patent applications covered by this definition. Any one of the foregoing is a “Patent”.
