[Stuart]

BBC America is jointly owned by BBC Studios and AMC Networks. It primarily airs sci-fi and action series and films, as well as selected programmes from the BBC.  It operates as a commercially-supported channel and accepts traditional advertising. It is also funded by television subscription fees.

BBC First (Canada) is wholly owned by Blue Ant Media, a Canadian broadcasting and media company. It broadcasts a variety of drama, comedy, and film programming originating primarily from the BBC. It is an entirely different animal from BBC America. 

BBC First (Canada) probably broadcast much of the content from the domestic UK television over the weekend as the late Queen was also Head of State of Canada.

BBC First elsewhere in the world is an entertainment subscription television channel featuring comedy, crime, drama and film programming, originating from UK and mostly from the BBC. The channel is wholly owned and operated by BBC Studios as is BBC Entertainment which has similar programming, but also draws on those from Channel 4 and other UK producers..

BBC Brit is also a subscription television channel featuring factual entertainment programming. The channel is wholly owned and operated by BBC Studios.

BBC Earth is a documentary subscription television channel featuring premium factual programming.  The channel is wholly owned and operated by BBC Studios, but has closed in some regions.

BBC Lifestyle is an international television channel wholly owned by BBC Studios. The channel provides six programming strands: Food, Home & Design, Fashion & Style, Health, Parenting, and Personal Development. It has also closed in some regions.

We all know what's happening with BBC World News.

EDIT:

Oops, I forgot 'BBC UKTV' which is an Australian pay television channel in Australia and New Zealand, screening British entertainment programming, sourced mainly from the archives of the the BBC, RTL Group (mainly Talkback Thames material) and ITV plc. It is now owned solely by BBC Studios.