The pumpkin and many garden squashes including, Spaghetti, Crookneck, Zucchini, Sweet Dumpling, Patty Pan, Heart of Gold, Gem, Dilicata and Acorn are all the same species; Cucurbita pepo. These will all cross pollinate readily and usually do if grown anywhere near each other. The next generation of plants will be squash, but no telling what they will look like or taste like. I treat all volunteer squash as weeds. I would rather pay a few cents for some seed and know what I am getting.
Butternut is a different species; Cucurbita moschata, and it is said it will not cross with the others. I am making that test this season as I planted some seed from a wintered over Butternut Squash. I will report on that when I see the fruit. There was a good variety of squash grown near by last year.
I have heard that gourds will cross with the squash, but can't substantiate that. Gourds are of the genus Lagenaria. I am growing some bottle gourds this season and will save some seed and see if it crossed or not. I have grown the little decorative gourds before and saved seed. It never comes the same the following year. Maybe I had a packet of mixed variety gourds ? I can't remember. I haven't grown gourds for a long time.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-