Over time the meanings of sympathy and empathy have swapped. Sympathy meant "feeling with", the ability to experience another person's feelings, whereas empathy meant the ability to intuit another person's feelings from observation.
Saying that autistic people lack empathy (in this sense) was an oversimplification. This became outright ableist with the idea that autistic people are incapable of sympathy, and therefore lack a "theory of mind", which isn't true at all.