I recently learned that some varieties of popcorn planted next to sweetcorn will give you the same variety if you save from the popcorn (the sweetcorn seed will be crossed). What's happening is that the popcorn can only be pollinated by that popcorn's pollen, the sweetcorn can be pollinated by the popcorn. It's called the "gametophytic incompatibility gene" or Ga1, some varieties of popcorn have it some don't. If you have a popcorn variety that has the gene, you can save your popcorn seed for replanting, but not your sweetcorn. What variety of popcorn do you have?
If your popcorn and sweetcorn do cross, the resulting corn plants will produce corn suitable for neither popcorn or sweetcorn. The two types of corn have different kinds of starches in different parts in the kernel, along with different levels of sugars - this gives them the ability to popcorn/have texture and flavor of sweetcorn. Crossing between the two will mess up the type and arrangement of the starches and change their ability to pop/have taste and texture of sweet corn.