Alerting profiles is a new feature that allows to filter the outgoing problem alerts by different criteria such as problem severity, problem duration and tags.
The Alerting profile filtering can apply to all notifications channels, such as Dynatrace Mobile App, Web UI, Slack, email, HipChat, etc.
Custom alerts on the other hand are threshold definitions that open customized alerts depending on metrics you choose.
Here is Wolfgang's blog post that just came out for alerting profiles as well: https://www.dynatrace.com/blog/efficiently-filter-problem-notifications-with-alerting-profiles/
I came across these in our demo environment yesterday, and am glad I waited before asking about them!