It's very different over here. Every state, and often individual cities, have their own rules and fees,
but generally speaking a random alpha-numeric plate is issued when a vehicle is registered. (usually 6 spaces, California uses 7) Cost is typically based on a percentage of the vehicles taxable value, so cost varies greatly.
Also, it is usually an annually recurring fee. (and often an annual inspection of some type)
Then it gets really involved.
Using Colorado as an example, You have a basic no-frills plate that is similar to Itsky's, but is green mountains with white sky and lettering.
For an additional fee (ranging from a one time $50 fee to a recurring annual $85 fee)
You can choose from one of about 30 different "specialty" plates with subjects ranging from
Collector Vehicle
Breast Cancer Awareness
Adopt a shelter pet
Support your local horse
10th Mountain Armoured Division
County specific colour schemes
University of Northern Colorado (like Itsky's)
etc etc.
Then, for an ADDITIONAL fee, you can apply for personalized plates. You submit your requested plate, and wait for the state to get back to you. If the plate you requested is available, and meets their subjective appropriateness qualifications, (ie: non-offensive) you pay a one time fee to secure/manufacture the plate ($75) then $50 annually in addition to basic registration costs.

It is illegal to sell a vehicle with "your" plates still attached.
You may transfer your plate to a different vehicle, but if it is not re-registered to another vehicle before expiring, it is void, and your # and or specialized text goes back up for grabs.

Across the United States, there may be over a thousand visually different plates.
Very different.