Does this mean place some cookie dough every 4 inches (i.e. 4 inches center-to-center), or have a 4 inch gap between each cookie?
It means to have a 4 inch gap between each cookie. Of course, if you use less dough per cookie, you can put them a bit closer together.
Normally, if you put cookie dough on the tray, the surface of the cookie won't be very big (perhaps an inch). So it would not make a very big difference if you would've placed the cookies 4 inches apart center-to-center. Just be careful during the first batch. If you see you have a lot of space between the finished cookies, you can put the dough closer together for the next batch (if you use the same amount of dough per cookie).