Branching Factor

Hey folks, I''m interested in the notion of what we mean when we say "Branching Factor" in relation to game trees. When we look at data-structures in general we usually talk about the degree of the node or tree - the amount of child nodes a parent node has or the maximum alowed in a tree respectively. Sometimes we also say the "arity" of the tree. But with game-trees, the tree wont exist in memory, rather it is created and destroyed on the fly by the iterative nature of the minimax algorithm (or some variation of it). So, is the term "branching factor" exclusive to an algorithmic construction of a tree as in the game tree, or can we say that an "in memory" construction of a tree has a branching factor too? Also, is there a general way of destinguishing between these to notions of trees - ie: do they each have names? Sorry for the academia, im writing a research thing for college and I havnt found anything on this... Thanks. Tim.