Stakes Races - the highest class of American racing
Stakes races are the highest grade of USA horse races, but even these are broken down into sub-divisions:

Grade 1: These are the best races run in America and they obviously carry the highest prize-money. All the major races (such as the Triple Crown races and Breeders Cup) are Grade 1 Stakes races.

Grade 2: This one notch below Grade 1 races but some horses can never bridge the gap between Grade 2 races and the very highest class.

Grade 3: Grade 3 types, unless they are on an upward curve and improving through the racing ranks, often struggle in higher grade. A true Grade 1 thoroughbred tends to be at least 15 pounds better than a horse that has the ability to win a Grade 3, but no more.

If you are trying to assess race form and past performances be very wary of any horse rising in class that has not already won cosily in lesser grade. He will invariably be outclassed. Conversely horses with form in say Grade 1 races might be of great interest when dropping to Grade 2 Stakes races.

Allowance Races - one level below Grade 3 Stakes races
Below Grade 3 Stakes races are allowance races, and in similar vein to stakes races, allowance races are broken down by class:

N4X allowance races: These races are for horses who have not won more than three allowance races (ie: non-winners of four allowance races)

N3X allowance races: These races are for horses who are non-winners of three allowance races ie: they can have won two allowance races.

N2X allowance races: These races are for horses who have not won more than one allowance races.

N1X allowance races: These races are for horses who must not have won an allowance race or in any higher grade. Put another way, it is for non-winners of a race other than a maiden or claiming race.

Claiming Races
Around 50% of horse races in America are claiming races. In a claiming race a price is put on the head of a horse (the lowest price level is around $2000). At the top end of claiming races the price put on the head of the horse may be say $50,000. These latter races would obviously attract better quality horses than the the $2000 claimers. That is because anyone can purchase (or 'claim') a horse in a claiming race for that price.

Unlike in the United Kingdom, where claims are made after the race is run. In the United States the claim goes in before the race is run. This means there is an element of a gamble if you make a claim for a horse. You may claim the favorite for the race beforehand, only to see the horse trail in last. You will have bought that horse.

Claiming races may feature horses dropping in grade from allowance or even stakes level. There may be many reasons for this, including: connections want to sell the horse; connections want to get some easy prizemoney pickings; the horse is losing its previous higher level of form.

Horses may also go into claimers after they have won their maiden (or even a maiden claiming race) if connections believe that is where their level of ability lies. That said, there are examples of champions with millions of dollars of earnings (like Lava Man) that were first claimed out of small-time claiming races. That is a scenario that may make the former owners feel like they gave away a winning lottery ticket.