Dot product versus matrix multiplication, is the later a special case of the first?

Dot product is defined between two vectors.

Matrix product is defined between two matrices.

They are different operations between different objects.

The connection between the two operations that comes to my mind is the following: To calculate the $c_{i,j}$ entry of the matrix $C:=AB$, one takes the dot product of the $i$'th row of the matrix $A$ with the $j$'th column of the matrix $B.$