Somewhat close.
Lets say you perform a reaction and have your product x (which you want to isolate) along with some impurities y all in a solution of solvent A. Let's denote this as:
A(x,y), which means x and y are disolved in A.
Now we add solvent B and perform either an extraction or wash
Extraction:
When we add B to A, mix, then separate A and B, we get:
A(y) and B(x)
Your product is now out of your original reaction mixture (A) and in a new solvent (B). Plus, the impurities have been removed since they stay in solvent A. Here, you discard solvent A and isolate your compound from solvent B.
Wash:
When we add B to A, mix, then separate A and B, we get:
A(x) and B(y)
Your product is still in A, but all of your impurities have been removed by solvent B. Here, you discard solvent B and isolate your compound from solvent A.