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Every horse starts it's life with a certain "base score" which is, in simple terms, the number the judge assigns to it that determines where it places in the class. This score is affected by the horse's Consistency, meaning how much it's score in a class varies from one show to the next during a given week between trainings. Horses that receive a Consistent rating from the Consistency Test may have scores that range from perfectly consistent, meaning it's score never varies in a given week, up to +/-2, meaning that it's show score may be up to two points higher than the base score or or up to two points lower than the base score, a total range of 5 points. Inconsistent horses may have their scores varying by a wider amount, but everything is truly random, so an inconsistent horse may go quite some time without a wide swing. Some horses have been seen that are classed "Very Inconsistent". It is virtually impossible to calculate what their base score might be.

Every time a horse is trained a certain number of points are added to its base score, generating a new mark for its potential score in a class. The average foundation horse gains about 3 points with each weekly training. The number of points added with training increases as the PT level of horses increase. The PT level of a horse remains the same throughout its life. Horses continue to add points to their show score until they "level off," usually about the time when their age reaches the number of their PT score. At this time, training will add tiny fractions to the show score, so some horses may still level up into a higher class if they live long enough.

As a horse is trained each week, it gradually works its way up through the various Levels and Grades in the showing system. There are 8 showing levels and each level contains 4 grades (Local, Regional, National, and World, abbreviated L, R, N, and W). This gives a total of 32 showing level/grades. Only the horses with the highest PT scores are likely to reach the top level, Grand Prix World.

This page contains a chart that shows all the levels and grades with entry fees and maximum number of horses in a class. http://hj2.huntandjump.com/entries.php

I think it is the the Level/Grade number that you are referring to in your question about letters following a number.
Here is a sample horse to make it easier to see what I'm talking about below:

http://hj2.huntandjump.com/horse.php?horseid=26507

The Level/Grade position of a horse is given in two ways. On the horse's Info tab you will find the formal designation of it's current showing level. For Charlis Delhi it is currently "Level: Training, Grade: Regional. In other places, this information is abbreviated by giving the number of the level and a letter indicating the grade. On the barn page, for instance, in the column following the horse's Size, it is given as 4R.

On his Records tab, his showing history is given. Each line is the information for one class. This includes, from left to right, the name of the class; its date; its Level Grade, given by number and letter; the horse's place in that class; and the score it was given by the "judge" (a random number generated by the program based on the horse's base score at the time and its consistency rating).

You will notice that the names of the recent classes are links. Clicking on one will take you to the complete records for that class. There you will find a list of all the horses entered in that class. It columns include where each one placed, its name, what its show score was, who owns it, how many points were added to their collection of show points (NOT the same as the points in their show score, but the awards given for where they placed in that class) and how many hajibucks they earned. Horses that are in the top half of the class earn a profit, the rest make less money than the entry fee for the class.

The MOST important part of this information is the points awarded for where the horse placed in the class. These points accumulate throughout the life of the horse and remain with it even when it is sold to another player. Each week you will receive a Showing Bonus, which in HaJ2 is currently 75% of the total number of points all your horses have accumulated in their lifetimes. Small stables need to keep an eye on their profit/loss from showing, which is calculated by comparing the entry fees paid with the hajibucks all their horses have won in their shows. Once a certain point has been reached, the showing bonus will surpass the profit/loss figure and you will not have to worry about stable income unless you get really extravagant. Simply put, the more horses you have showing, the better off you will be, because a horse adds points every time it shows except when it comes in last.