It used to be two companies, but later they merged

But not everything was merged, just the assets were merged, and they were all managed by Vivendi Group

However, their companies themselves still do their own things and do not interfere between them. They can be interpreted as Activision Blizzard Company, which is the same name, followed by Blizzard Branch and Activision Branch

Call of Duty is made by Activision, and Warcraft is made by Blizzard.

Blizzard Entertainment is a famous video game production and distribution company. It was founded on February 8, 1991 by three graduates of the University of California, Los Angeles. Michael Morhaime, Allen Adham, and Frank Pearce founded it under the name Silicon&Synapse; in 1994, the brand was officially renamed "Blizzard".

Reference: Blizzard Entertainment_Baidu Encyclopedia