The oud and the guitar are strung similarly (six strings vs. six courses of strings), and are both played with a flat pick; but the guitar pick is much smaller and flatter than the risha used for the oud. Did the different picks for the different instruments evolve by accident, or is the oud somehow better suited to playing with a risha and the guitar better suited to the triangular guitar pick? Could you reasonably play a guitar with a risha, or vice versa?
The modern guitar and oud were developed in different countries and so were developed with different playing styles in mind. The guitar plectrum and oud risha were likely just developed by different people and at different times in history.
In terms of playing today, playing with these tools is likely just due to tradition and the timbre of the instrument when played with these tools. The point of the risha sticks out towards the end of the thumb when held in a traditional way, and the guitar plectrum typically sticks out at a right angle to the thumb when held traditionally. These techniques create different sounds when striking a string. See picture 1 (from oudforguitarists) vs picture 2 (from justinguitar):
However, any instrument can be played with any tool you want to use - see Jimmy Page playing guitar with a violin bow or Paul Gilbert playing guitar with an electric drill in the solo to Mr Big - "Daddy, Brother, Lover, Little Boy" (starting around 2:20).