Though this is old, I think question is valid even today
My suspicion is that aud should refer to the resource server(s), and the client_id should refer to one of the client applications recognized by the authentication server
Yes, aud should refer to token consuming party. And client_id refers to token obtaining party.
In my current case, my resource server is also my web app client.
In the OP's scenario, web app and resource server both belongs to same party. So this means client and audience to be same. But there can be situations where this is not the case.
Think about a SPA which consume an OAuth protected resource. In this scenario SPA is the client. Protected resource is the audience of access token.
This second scenario is interesting. There is a working draft in place named "Resource Indicators for OAuth 2.0" which explain where you can define the intended audience in your authorisation request. So the resulting token will restricted to the specified audience. Also, Azure OIDC use a similar approach where it allows resource registration and allow auth request to contain resource parameter to define access token intended audience. Such mechanisms allow OAuth adpotations to have a separation between client and token consuming (audience) party.