The implicit grant is a simplified authorization code flow optimized for clients implemented in a browser using a scripting language such as JavaScript.
The resource owner password credentials (i.e., username and password) can be used directly as an authorization grant to obtain an access token.
(https://tools.ietf.org/html/rfc6749#section-1.2)
My question is about understanding how these two grant types are different?
As you quoted, the "Resource Owner Password Credentials Grant" is suitable in cases where the resource owner has a trust relationship with the client, such as the device operating system. An example is Facebook application - Facebook trusts their app that is installed on the device.
Thus, client-app does not have to be registered in the auth-server. As you can see in the request the client_id is not transferred as a param. In addition, the flow is simpler - the access token is retrieved within a single request.
Important to understand here is the way and place you enter your credentials.
Implicit
Your app is https://example.com and for authentication, you are going to https://auth.some-domain.com (or even https://auth.example.com). After successful authentication, user is redirected to https://example.com/some-callbackurl?#token=token-value.
Points to be noted: Redirection and token in URL
Resource Owner Password flow
Your app is https://example.com and for authentication, you are going to https://example.com (or https://example.com/login). After successful authentication, user is redirected to https://example.com/home.
Points to be noted: No redirection and no token exchange in URL
Basically if you are owning the app (client app, server app, auth app) then this is something you would do. Basically you are the one who is in charge of authentication - not a third party app. You trust your client app.
https://example.com/login gets credentials from user and does a HTTP REST POST (for example) call and get a response as token (and refresh token - optionally). It saves it in localStorage or cookie and then redirects to home page or whatever page it has to redirect to.
No redirection happens in exchange.
