AspectJ is the industry-standard implementation for Aspect Oriented Programming whereas Spring implements AOP for some cases.
Main differences between Spring AOP and AspectJ are:
Spring AOP is simpler to use than AspectJ because we don’t need to worry about the weaving process.
Spring AOP supports AspectJ annotations, so if you are familiar with AspectJ then working with Spring AOP is easier.
Spring AOP supports only proxy-based AOP, so it can be applied only to method execution join points. AspectJ support all kinds of point cuts.
One of the shortcoming of Spring AOP is that it can be applied only to the beans created through Spring Context.