Concrete curb after driveway poured
I'm sure they did something to connect the to. Rebar pins....Pic would be helpful but, in a case like this you would have a crack going the length of it. Its called a cold joint. You should cut a control joint down it, so it's straight. If it's a very large crack (you can fit a credit card in it), it need to be removed. Caulking, if you want to caulk the control joint that's fine, just make it bigger than a typical cut joint. Also, they don't sell a caulking at home depot or lowes that will work. That's stuff that makes you think it's caulking, but it's a nice way for them to take your money instead of robbing you at gun point. Find a specialty concrete supply store and buy a self leveling caulking from them.