DragonKing: It's entirely arbitrary. On a board in live play there will always be one player going clockwise and one going anti-clockwise. It's only possible for both players to makes their moves in the same direction if they each have a board, which is, of course, how it is on a game site.

In books it's likely to be the preference of the author. For a game site it may be their preference or it may be that they take their convention from elsewhere. Some sites, such as DailyGammon, allow each player to choose their direction of play.