Ternary operator just means that the operator takes three operands. There are unary operators (such as the minus sign in front of an expression) and binary operators (such as a division sign between two expressions).
I think that ?: may be the only ternary operator in C/C++. I am not sure that the operator has a formal name although conditional operator fits, but ?: is known informally as the "Elvis operator". (Look at it sideways and with a lot of imagination.)