I can't move the thread, but I can try to answer the question...
The short answer is that it's different, and likely not as powerful as in CivRev.
The long answer is that in Civ 4, there are multiple ways of rushing things:
a) You can rush units and buildings with gold, if you are running the Universal Suffrage civic.
b) You can rush units and buildings with population, if you are running the Slavery civic. The city population will be more unhappy for a while. Very useful early on as you will often hit your happy cap early and enslaving useless angry population doesn't hurt. Also it's often one of the first civics you unlock, by researching Bronze Working.
c) You can draft units out of band for population, if you are running the Nationhood civic. The city population will be more unhappy for a while. The units will start with less experience than regularly built units would in that city. Nice in a high-food city with Globe Theatre.
With a) and b), the build completes at the end of your turn (so a rush-bought unit will still be able to defend the city). With c), you get the unit instantly, before the end of the turn.
Also note that c) will not let you choose what to draft, you will get something that can defend a city, e.g. longbowmen, riflemen and so on, whichever is the most modern unit in that line that you can build. Neither choice will allow you to rush projects (such as Apollo).