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Difference Between Shift Adder and Serial Adder

Are Shift Adders and Serial Adders the same? I've tried googling but I don't understand the difference. I have to use it in VHDL.

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Serial Binary Adder : A serial binary adder, or bit-to-serial adder, is a digital circuit that performs binary addition on bits. For example, to add 1010 + 0100, we will start with LSB.

0 + 0 --> 0 
1 + 0 --> 1 
0 + 1 --> 1 
1 + 0 --> 1

And your final answer is 1110.

Shift Adder : Used for multiplication. For example, if we want to multiply 10 and 10, we will start with the LSB.



10 * 0 --> 00
10 * 1 --> 10

The first partial product is shifted to the right before being added to the second partial product. To get the result.

 000
+10
-------
 100
+1


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