Two versions of TimescaleDB are available: TimescaleDB Community Edition, licensed under the Timescale License, and TimescaleDB Apache 2 Edition.
TimescaleDB Community Edition is the most recent and complete version of TimescaleDB, including all the latest features, and it is completely free if you manage your own service. You also have the “right to repair” and make modifications to the source code.
The main difference between the TimescaleDB Community Edition and TimescaleDB Apache 2 Edition is that the Timescale License prevents third parties to sell TimescaleDB Community Edition as a service, while TimescaleDB Apache 2 is completely unrestricted in this regard. For more information about the TimescaleDB licensing, please consult this docs page.
In the case of Promscale, it is available under the Apache 2 open source license. For the latest information about Promscale licensing see the Promscale repo.