From the documentation:
startup_clauses let you mount and open the database so that it is accessible to users.
MOUNT clause to mount the database. Do not use this clause when the database is already mounted.
MOUNT STANDBY DATABASE
You can specify
MOUNT STANDBY DATABASE to mount a physical standby database. The keywords
STANDBY DATABASE are optional, because Oracle Database determines automatically whether the database to be mounted is a primary or standby database. As soon as this statement executes, the standby instance can receive redo data from the primary instance.
startup mount is the same as
startup nomount; alter database mount.
So there is no practical difference between the two approaches you showed, if the commands are run consecutively (i.e. you are not doing anything else while it is started but not mounted). However, including
STANDBY DATABASE in the command clearly shows intent, so I think it's generally better to include it, particularly if you're scripting this as part of a switchover process.