I'm not sure exactly what you are asking, but cities produce only based on what tiles their citizens work, specialists run, and trade routes. They don't share this but both contribute to the overall empire.
If you are referring to overlap of two cities based on the tiles in the BFC, only one city can work a tile shared by both cities. You have to go into the city screen and "unfog" a certain tile for a citizen to work it. That tile will then not be available to the other city. This can actually be beneficial to share a few tiles so that one city can work a cottage or two until the other city has enough citizens to take the cottages back on. This allows the cottages to continue growing.
If you question is generally about what connects cities so that trade routes are created and resources shared, that is not a result of cultural borders but rather roads, rivers, and coastal trade, in which case you need sailing. One thing of note is that early game if you have two cities build on tiles adjacent to the same river, you do not have to worry about wasting worker turns on a road between the two cities as the river will connect the trade route. Later on though you may want a road simply for the purposed of faster troop movement, but early game worker turns are gold. (Also, note that if one of these cites is simply a tile or two off a river but some distance from the cap you can simply build a road to the river to connect it as well.
