"Company traffic" is the idiom for "an aircraft with the same callsign" ... that would be American, Delta, Southwest, or whatever. You will often hear it on Ground, such as "taxi via bravo echo, follow the company 737".
Here we have Whatever 924 and Whatever 928. You might also have American 27 and United 27. These are very close.
When the controller knows that callsigns that might be confused are on frequency, they will usually alert the aircrews. The purpose of this is to ensure that the crew listens carefully to the callsigns and does not follow a clearance meant for another aircraft.