@akelad bot framework is basically the SDK, that allows you to connect to Cognitive services like NLU, speech, vision etc along with a dispatcher for orchestrating conversations using Activity tracker. I would compare it to botkit. Bot framework can be hosted anywhere as well as a node js or C# app or with Docker.
However Azure Web Bot service is the azure web service where you have botframework out of the box for the connectors. I would use this picture below to give an idea. As you can see you are using Azure Bot Service to connect to channels or devices. You could host the botframework app on azure bot service. In the case of the Rasa botframework connector, the connector is written to connect to azure bot service where i could simply plug in Rasa Bot to the Azure Bot service to connect to the channels without using botframework sdk at all.
On another instance, I am using Botframework sdk for vision and using the rest connector of rasa for the chatbot, hosting it on docker, and connecting it to azure bot service which then connects to Teams.