They are different concepts. They overlap pretty often, but they are different.
Recursion happens whenever a function calls itself, directly or indirectly. This is all.
Example:
a -> call a
a -> call b, b -> call c, c -> call a
Dynamic programming is when you use solutions to smaller subproblems in order to solve a larger problem. This is easiest to implement recursively because you usually think of such solutions in terms of a recursive function. An iterative implementation is usually preferred though, because it takes less time and memory.
Memoization is used to prevent recursive DP implementation from taking a lot more time than needed. Most times, a DP algorithm will use the same subproblem in solving multiple large problems. In a recursive implementation, this means we will recompute the same thing multiple times. Memoization implies saving the results of these subproblems into a table. When entering a recursive call, we check if its result exists in the table: if yes, we return it, if not, we compute it, save it in the table, and then return it.
