Both involve taking cards from the deck.
Fetch seems to be related to “searching” for a card, while Draw is just the top card.
Does a Fetched card count as a Drawn card (ie creature gains +1/+1 every time you draw a card)?
Fetching is not considered a card draw and will not trigger such abilities.
Fetch for example won’t trigger Ob Nixilis’ 3rd ability, either.
Fetch is a way to weaken certain cards. I really want to play Tower Geist in a Rattlechains deck, but the extra card it gets doesn’t benefit from the reduced cost effect. This is also the reason I almost never play Talent of the Telepath in any deck that cares about drawn cards like Sage or Sphinx’s Tutelage, despite it being one of the strongest cards in a vacuum.