There are four hotbar-related text commands which set actions.
/hotbar
>>Subcommands
action "action name" [#1] [#2]
/pvphotbar
>>Subcommands
action "action name" [#1] [#2]
/crosshotbar
>>Subcommands
set "action name" [number] [slot name]
/pvpcrosshotbar
>>Subcommands
set "action name" [number] [slot name]
In the English version, "action" is used in the description of hotbar, while "set" is used in the description of crosshotbar. In fact, both "action" and "set" are accepted as valid subcommands in all of these text commands.

In the Japanese version, "set(action)" is used consistently instead of "action" or "set" in the descriptions of these text commands. I believe that "action" and "set" should be replaced with "set(action)".

Additionally, "PvP action name" is used instead of "action name" in the descriptions of /pvphotbar and /pvpcrosshotbar. I believe this wording is more appropriate.