Binary Adder and Parallel Adder
There is a distinction between parallel adder vs serial adder. Both are binary adders, of course, since are used on bit-represented numbers. Parallel adder is a combinatorial circuit (not clocked, does not have any memory and feedback) adding every bit position of the operands in the same time. Thus it is requiring number of bit-adders(full adders + 1 half adder) equal to the number of bits to be added. 

(The image taken from here)

Serial adder is a sequential circuit, consisting of a flip-flop and a full adder. At each clock cycle, it is taking the result of the previous bit addition result carry stored in the flip-flop, calculating the sum result and storing the carry to the flipflop for the next calculation. In this manner, the input data have to be fed serially, synchronized by the clock, and the result is read serially as well.
 
(The image taken from here)