And, there is also some confusion about the definitions of "heirloom" and "open-pollinated." My understanding is that an heirloom is an open-pollinated variety that has been saved and passed along for many years (although I don't think there's an official cut-off for the time), while open-pollinated varieties are any that will come back from seed and be the same as the parent plant over successive generations. Assuming, of course, that they haven't been allowed to cross pollinate with another variety, either a hybrid or OP type. It is also possible to grow out seeds of a hybrid over the course of multiple generations, selecting for the desired traits, and eventually obtain a stable OP variety.
And all of this is further confused by the fact that a number of the seed catalogs are offering somethiing called "Heirloom Marriage Hybrid Tomatoes." Meaning, presumably, that heirloom varieties have been crossed to obtain a new hybrid.
If you choose to save seeds from your plants, there is the potential for cross-pollination from other plants of the same species, whether they are in your garden or growing nearby. As an example, if you are saving carrot seed, your garden carrots could be cross-pollinated by the weed/wildflower Queen Anne's Lace. If you are saving seed from your pumpkins, and your next-door neighbor is growing pumpkins or a squash of the same species, bees could be carrying pollen from one garden to another. And if you are growing corn and happen to live near a farm that grows Roundup-Ready GMO corn, your corn could be cross pollinated by the GMO pollen and therefore produce seed that has the Roundup-Ready trait.