Summer squash, winter squash, pumpkins and gourds belong to the Cucurbita family. Members of this family may cross-pollinate with each other. (Insects can bring pollen from other plants to female flowers.)
However, the first year of a cross, the resulting fruit is completely normal looking and tasting. Only the end result seed carries the crossed gene. So, if you saved the seed and planted it the following year, you might get something strange as a result.
If you are growing plants to eat the fruit, you do not have to worry about cross-pollination in your home garden.