Wine grapes have a really thick pith inside and make seeds, table grapes generally have less pith and are seedless varieties. Here's a diagram. Harvesting them when ripe is the hard part, you have to take a random sample and check the sugar levels with refractometer. Iirc, 31 brix or so is fully ripe; less suitable varieties will peak at lower values.
Edit: Here are the exact parameters for wine grape harvest that would make good wine: "Brix: >24 ; TotalAcid .58 - .65 ; PH 3.4 – 3.6" from source.