Your question probably turns on not fully understanding "Ground". Ground can be "a common point in the circuit". Ground can be "A common point to make a building electrically safe". A place in an antenna system (typically vertical) which is the counterpoise for the radiator. Ground can also mean "The earth" --- a substantial connection to the surrounding surface" (the others involve this idea as well).
In your case, what you want is a place for excess charge to go. Assuming your house is adequately wired, the equipment ground or third prong of a power plug" suffices. One method I use is a power plug where the strap is ONLY connected to that equipment ground, but I verify that here is no current flowing from there to anywhere else. An other method is a cold water pipe. If I am installing a board or other component in a computer then, I touch the metal part of the computer before I bring in that part.
What you mainly want is no charge to flow from your body through the device you are working on. So - if it flows before hand directly, you are all set.
Here is a little experiment, assuming it's dry air where you are, shuffle your feat on the carpet and then touch something with your finger. You will feel "a shock". Now repeat with a ring and touching your ring. You will feel nothing. In both cases there is a charge transfer. "The shock" is actually the transfer creating a very small area of plasma gas which is what you feel. There isn't enough current to really shock you, though it feels that way. However, there is enough to ruin a chip either way.