Is there a difference if I were to evolve a pidgey into a pidgeot vs catching a pidgeot in the wild?
There are multiple.
The biggest one is that pokemon you evolve tend to have a higher CP than an already evolved pokemon in the wild but their maximum CP will always be the same. An exception would be if you evolved a pokemon when you're at level 5 but then you catch the same pokemon at level 10. Because your maximum CP for every pokemon is higher with trainer levels the pokemon you find also have higher CP.
The other reason is that you gain a fair amount of experience from evolving a pokemon. It is 500 experience per evolution and an extra 500 if the evolved pokemon is not something you have caught before.
I caught a Pigeoto and evolved a Pidgey but the wild one was still stronger; plus the wild one has better attacks. I do not understand it. Might as well evolve the wild Pigeoto at some point and just power up to max CP.