You can use either for browsing, but you can only edit things from https://toolsadmin.wikimedia.org/tools/id/checker. The reason for the split is that https://tools.wmflabs.org/ is an untrusted environment. That is the shared Toolforge environment and we can't allow it to have passwords that can edit the LDAP directory and other secure data stores. We also can't trust it as an environment where we can take people's LDAP passowrds for authentication.

The current split is really no different than the historical split between toolforge and wikitech.

In the long term we should consider consolidating around toolsadmin.wikimedia.org, rather than maintain two separate endpoints.