They may not be the variety you remember, You said it was quite a few years ago. If you want grapes I'd suggest you plant a known cultivar that has a history of producing nice fruit and is compatible with your climate zone. Otherwise you could end up with poor tasting fruit after training and waiting years to enjoy them.

Yes wild grape. Depending on your perspective it is both.

My first thought also. Genus amepelopsis.

"The muscadine grape is native to the southeastern United States and was the first native grape species to be cultivated in North America. The natural range of muscadine grapes extends from Delaware to central Florida and occurs in all states along the Gulf Coast to east Texas. It also extends northward along the Mississippi River to Missouri. Muscadine grapes will perform well throughout Florida, although performance is poor in calcareous soils or in soils with very poor drainage. Most scientists divide the Vitis genus into two subgenera: Euvitis (the European, Vitis vinifera L. grapes and the American bunch grapes, Vitis labrusca L.) and the Muscadania grapes (muscadine grapes). There are three species within the Muscadania subgenera (Vitis munsoniana, Vitis popenoei and Vitis rotundifolia)."