api.md: make it clearer where to get the tailnet name in API calls

We added the tailnet organization name to to the settings page with
tailscale/corp#6977, but the docs were not updated to reflect this.
We later also changed "tailnet name" to refer to the MagicDNS hostname
(tailscale/corp#7537), which further confuses things (see https://stackoverflow.com/questions/74132318).

Make it slightly clearer what is the expected value for tailnet names in
API calls and how to get it.

Signed-off-by: Mihai Parparita <mihai@tailscale.com>

api.md

@@ -335,11 +335,12 @@ The response is 2xx on success. The response body is currently an empty JSON
 object.
 
 ## Tailnet
-A tailnet is the name of your Tailscale network.
-You can find it in the top left corner of the [Admin Panel](https://login.tailscale.com/admin) beside the Tailscale logo.
 
+A tailnet is your private network, composed of all the devices on it and their configuration. For more information on tailnets, see [our user-facing documentation](https://tailscale.com/kb/1136/tailnet/).
 
-`alice@example.com` belongs to the `example.com` tailnet and would use the following format for API calls:
+When making API requests, your tailnet is identified by the organization name. You can find it on the [Settings page](https://login.tailscale.com/admin/settings) of the admin console.
+
+For example, if `alice@example.com` belongs to the `example.com` tailnet, they would use the following format for API calls:
 
 ```
 GET /api/v2/tailnet/example.com/...
@@ -364,8 +365,6 @@ curl https://api.tailscale.com/api/v2/tailnet/-/...
 
 Tailnets are a top-level resource. ACL is an example of a resource that is tied to a top-level tailnet.
 
-For more information on Tailscale networks/tailnets, click [here](https://tailscale.com/kb/1064/invite-team-members).
-
 ### ACL
 
 <a name=tailnet-acl-get></a>