My understanding of both starts with this model:
which has two random variables whose individual distributions are shown in red and blue, and their join distribution shown in green.
I'm comfortable with the idea of using discrete math to take subsets of the tuples in the joint distribution, then using those subsets as the domain for various functions ( vis. functions that give probabilities and calculate statistics ).
Then, amongst those functions we have two kinds in particular that have names: the marginal distribution functions and conditional probability distribution functions.
My current understanding is that conditional probability distribution functions take a subset of tuples that range over both features of the tuple--x and y, say. You'll use conditional probability distribution functions to calculate probabilities given some subset of x and some subset of y.
Then, my current understanding of marginal distribution functions is that they do the same thing as conditional probability distribution functions, but lock one of the features down to a specific value.
Is that correct? I know I'm not using the standard set of jargon, but--I'm coming to statistics from pure math and computer science. So, forgive me while I try to connect one domain to another in my head.