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Could anyone tell me the definition of a Character in 40k?
There are a couple of references to what happens when a Character (not an Independent Character) leads a unit.
Pages 50-51 of the BGB. The first bullet under "Characters In Battle" describes what (non-Independent) Characters are. The entry "Characters As Leaders" gives more information on the same topic.
Simply put, they're just squad leaders or upgrades, not solo models like ICs are. Units with a Character use that Character's Ld value That Character can never leave the unit they were purchased for. And Characters are invisible within a unit - ie, they cannot be individually picked out in melee like Independent Characters can me.