Public portal is a type of license, where as WebLink is a product. WebLink can be used with a server that has a public portal license, which is the case you described for your public site with anonymous login. WebLink can also be used with regular licensed users if you do not have a public portal license on the server you are connecting to, if you have an number of insufficient public portal licenses, or if a user is not marked as read-only.
From the help files:
Any user (whether a Laserfiche user, a Windows user, or an LDAP user) who has been marked as a Read-Only user in the Administration Console will automatically use the Public Portal license.
If that user has been allocated a Named User license, the Laserfiche Server will attempt to connect them using the Public Portal license first. However, if the Public Portal license is a limited license and all connections are in use, the Laserfiche Server will then connect them using their allocated Named User license.
If a user accessing WebLink has not been marked as Read-Only in the Administration Console, they will not be able to connect using the Public Portal license. If the user has a Named User license, that license will be used when logging in to WebLink. If the user does not have a Named User license, they will not be able to log in.