Both actor-observer bias and self-serving bias are types of cognitive bias. Although they both help to explain our behavior, they are quite distinct.
Self-serving bias explains how we analyze the way we have behaved, depending on whether the outcome is positive or negative. For example, if we perform well in an examination, we are likely to credit ourselves, whereas if we perform badly, we will criticize the questions, our health, or other external factors.
Actor-observer bias describes how we attribute the cause of undesirable behavior in others to their own characteristics and our own undesirable behavior to external factors. If we (the actor) are late for a meeting, we might blame the traffic or other drivers, but if someone else is late, we (the observer) blame their lack of planning or foresight.