A Brine-Cured Ham (aka City Ham) is one that is cured either by soaking it in brine, or by having brine injected into it. Injection is a fast, reliable curing process.
In America, if a brine-cured ham says "with natural juices", it means it hasn't been injected, and the weight will be at least 18.5% protein. If it doesn't, part of its weight may be up to 10% in injected water, though it must still by law be at least 17% protein.
The ham may be sold needing full cooking, or it may be sold already partially cooked, or it may be cooked and ready to eat.
It may be sold whole, or if already cooked, packaged in slices for sandwiches.
"Partially-cooked" means it was heated to an internal temperature of at least 137 F (58 C) -- that being the temperature that the parasite "trichina" is killed at. Most processors cook to about 140 F (60) to be safe. But, further cooking for other nasties is still required -- the absolute minimum safe internal temperature under controlled laboratory conditions for pork is 150°F (66 C.)
Most health authorities advise higher, to allow for the vagaries of our ovens and oven thermostats, etc.
City Ham is a southern US term for Brine-Cured Ham.
Some refer to Brine-Cured Ham as "wet-cured ham."