Term or factor? I was reading a book on probability and encountered a summation expression like
$$P(Y\mid X, Z) = \sum_{W}P(Y\mid X, Z, W)P(W\mid X,Z)$$
followed by the author referring to "terms of the summation". My understanding has been that term typically refer to operands of an addition expression, whereas factor denotes an argument to a product, e.g. $A, x$ in $Ax + b$. Are these terms interchangeable or applicable to distinct contexts, and does it matter?

Certainly the word "factor" means something that gets multiplied.  Thus, in the expression $abcd$, the number $a$ is a factor.
I was taught in 8th grade that "terms" are things that get added or subtracted, and I've adhered to that usage ever since.  And the expression "collect like terms" is consistent with that.  But I've seen some authors occasionally using the word "term" to refer to factors in expressions like $\displaystyle\prod_{i\in I}a_i$.
