6 speed derailleur works for 7 speed cog? I am confused with description it say 6 speed, but below mention 7 speed as well.
Will this derailleur work on 7 speed freewheel?
Shimano derailleurs marketed as 7, 8, 9 speed (and in addition, 10 speed road), can be interchanged in any of those speed drivetrains. Six speed is included in there as well, it's just not common to see. So yes, a six speed rear derailleur will work correctly with 7, 8 or 9 rear speed systems. The derailleurs in these speed groups will all move the same amount based on the amount of cable pulled by the shifter. A limitation of the derailleur can be the size of smallest and largest rear cogs it can handle.  So you might put a six speed derailleur in a 9 speed drivetrain with an 11-34 tooth cassette, and it may shift in the middle of the cassette just fine but will not be able to get the chain on the extreme cogs because it's not designed to handle such extremes which don't exist in a 6 speed system.  So, it's not totally correct to say, ya you can use any of these derailleurs in any of these speed drivetrains because other considerations are necessary to address.
In general, a 6 speed derailleur CAN work in 7 speed drivetrain.