What is the difference between race/road and cx bikes? The only differences I know is that road bikes are often lighter and uses different set of brakes. But what else are the main differences?
Cyclocross bikes will have a slightly different geometry. More like a relaxed road geometry with a higher bottom bracket than a road bike typically. You'll be stretched out a bit less and more upright. Cross frames also will have wider tire clearances for 32mm to 35mm tires, but it varies by model as some can fit 38mm to 45mm tires.   

Traditionally, brakes tend to be wide profile cantilever brakes for good tire clearance and less chance of clogging with mud on cyclocross bikes.  However, disc brakes are now readily available on many cyclocross bikes.  Road / Racing bikes tend to use caliper brakes which have better modulation, but typically have small tire clearances, which may be too restrictive for cross tires, especially when they are covered in mud.

The new standard rear wheel size for disc cross bikes seems to be 135mm, so it's the same as mountain bike disc hubs. Non disc cyclocross bikes tend to have rear hubs which are spaced at 130mm, the current road standard hub spacing.  

Tires on a cross bike are going to be different as well.  Road bikes will typically have skinny 23mm to 28mm slicks.  On a cyclocross bike, you will typically have knobbier tires which may not last as long and provide more rolling resistance when compared to road tires, which is a tradeoff for having better handling on dirt / grass / mud.  You can always swap out tires to match whatever style of riding you prefer. Depending on how serious you are about racing, you can find both cyclocross and road tires available as glue on tubular tires.  However, some people have been adapting mountain bike tubeless technology and mounting cross tires as tubeless to run lower pressures for better offroad handling. It is not common to use the mountain bike style tubeless setup on a road bike, and generally not desirable.

Road bikes and cyclocross bikes tend to use STI shifters and similar groupsets (chainrings / cassette / derailleur combinations), however sometimes people prefer to use bar-end shifters for cyclocross (or retroshift shifters which mount bar end shifters on brake levers).  Additionally, some cyclocross bikes have an extra guard on the outer chainring to prevent injury when mounting / dismounting frequently. These guards are typically not as heavy duty as mountain bike bash guards.

Cable routing tends to be different on cyclocross bikes due to the need to shoulder a  bike during the race, so under the top tube routing is typically avoided.  Sometimes 3 cables on top of the top tube or internal cable routing strategies are used.  Often times full housing will be used to help prevent cables from getting contaminated with mud as easily.