Can a road bike's rear derailleur be used for either a 9 speed cassette or 10 speed cassette?
The spacing between 9 speed and 10 speed is controlled at the shift lever.

A 10 speed rear dérailleur will work with a 9 or 10 speed cassette and shifter. A 9 speed rear dérailleur is not compatible with 10 speed. 

The width of the chain and the cogs is the biggest issue. The pulleys on a 10 speed dérailleur are narrower, and a 10 speed chain will not rest correctly on the jockey pulleys of a 9 speed dérailleur. 

That does not mean it will not physically work, only that the shifting performance will be slow, you may drop gears unexpectedly, or have the chain skip unexpectedly.

Long story short, 10 speed should be 10 speed all the way throughout your bike for it to work consistently and properly.

Cable tension has nothing to do with cog spacing. That is designed into the shift lever. It is not adjustable, except by replacing the shifter.
I hope that helps.