Yes, mostly but it is used in a different way beyond serving content at low latency too. The term is also used for internet connected embedded devices who do not necessarily have a user.
Serverless stuff or V8 isolates do not always run in the edge but are able to run on the edge.
The difference between running on premise and running on the edge for serving content is that running on the edge has the same level of abstraction and dislocation as the cloud has. You do not know on what device stuff will run really.
The difference running embedded or running on the edge is that things runnings on the edge need to talk to some cloud and the cloud is important to the functionality of the device. Alexa boxes would be an example of such an edge device but so would be other embedded data acquisition devices which do some processing on board which is updated from and talking to the cloud.