There is a third type: structural home field advantage. Examples of these include Boise State's bright blue turf, Colorado teams playing home games at higher altitudes than most other teams, and hockey boards that bounce the puck certain ways.
Weather, altitude, blue turf, hockey boards, shooting background, etc I'd generally lump in under comfort and familiarity.
However, structural advantages do exist. The best example is actually MLB, where each team's field is shaped differently. The dimensions of the park impact hitters to an extent that it makes sense to tailor the roster composition to the yard at the margins: lefty hitters who loft many short flyballs in Yankee Stadium will hit homers that would be easy outs in most places, the typical left fielder won't be able to cover enough ground defensively in Pittsburgh, etc.
I was watching Ken Burns' Baseball many years ago and this reminded me of an interesting bit of trivia:
Many years ago, fans were allowed in the outfield at baseball games and were held back by a rope. A home run was when the ball flew (or rolled) past the rope.
Since the "line" was just a flexible rope, when the home team was batting the crowd would push the rope forward to help raise the odds of there being a home run. When the away team was batting, they would pull the rope back to lessen the odds.
Also, reminds me of the old Gatorade commercials with Old Shaq were he talks about how basketball changed (in the future) and he says "And then they put in the moving backboard..."
