What most often occurs in American gardens is that commonly-grown Halloween pumpkins (Cucurbita pepo) cross with commonly-grown zucchini (Cucurbita pepo). That accounts for your "pumpkini," Bud. Purdue University Cooperative Extension Service distributes this information provides a chart of the members of the cucurbit family grown in the US. And, gives the general outlines for cross-pollination: "Cross pollination generally occurs only among members within the same species. However some crossing between species occurs in the genus Cucurbita, among pumpkins, squash and gourds. C. pepo will cross with C. mixta and C. moschata: and C. maxima will cross with C. moschata. "C. pepo will not cross with C. maxima. "Cross pollination does not occur between melons, cucumbers or other species." University of Nebraska extension discusses a little about what they call the "folklore" of the Curbit Family & Cross-Pollination. I think that the key to your question is that different species generally do NOT cross with only a few exceptions. Human manipulation of cross-pollination is another story. Steve

Or will the melon come out ok, but the seeds of that melon will produce a mix of the two parents? Yes, the melon will be normal but the seeds in that melon, if planted next year, may produce a mixed product.

Banana melon and Canary types will cross. Kiwano melon is a unique species that will not cross with the other two.

Watermelons should all be able to cross with one another and muskmelons cross with each other (but watermelons won't cross with muskmelons). I've never tried saving seed from melons when I've grown more than one variety, but as I understand it you'll be very likely to get cross breeds if you do. The bees can't tell the difference. The farmers market melons are probably crossed too, assuming the farmer was just trying to get a good melon crop and wasn't worried about isolating varieties to save pure seed. Now, whether that means they're not worth planting depends on how you feel about growing melon mutts next year. They could be good, or they could be a great big waste of space. You really can't tell.