Basic Myhill-Nerode Theorem Practice
What you show is that $a$ and $b$ belong to the same equivalence class. Indeed, in this case there are exactly three equivalence classes: $\{\lambda\}$, $\{a,b\}$, and $\{ w : |w| \geq 2 \}$ (that's assuming the alphabet is $\{a,b\}$). I'll leave it as an exercise to prove that.

The Myhill–Nerode equivalence classes are intimately related to the minimal DFA. Indeed, given the minimal DFA, the number of equivalence classes equals the number of states, and each equivalence class consists of all strings which end up at that state. That's the quickest way to find the equivalence classes in simple cases such as $a+b$.