The posts in this thread don't make any damn sense, so I'm gonna answer the thread title instead:
There are in general 6 schemes for character advancement
- Level based
- Character point based
- Hybrid of points and level
- No Improvement
- Treasure Based
- MC fiat
In
Level Based advancement, all (or at least most) of the key abilities of characters are determined by one meta-number, called "level", apparently because Gygax did not own a thesaurus. When a character gains a level, they gain a large pile of bonuses and abilities that are added to the bonuses and abilities they already have. This is (largely) how D&D works. The major features of level based advancement are that there are few discrete packages of advancement, usually 20 or less, and never to my knowledge more than 50. Consequently players (generally) only have very few major choices to make when they gain advancement.
In
Character Point Based advancement, characters have a relatively large number of points to spend on a relatively wide selection of abilities and generally gain a few points to advance whatever they want each game session. Sometimes these points are exactly the same as those used in chargen (HERO, Gurps), other times there are radical and exploitable differences between the chargen points and the points handed out for advancement (Shadowrun, Storyteller, Feng Shui). In character point based advancement, characters are constantly receiving a small trickle of improvement and the players have a great deal of flexibility in applying that advancement. This allows for a lot of customization and allows characters to pick up small abilities related to their adventures frequently. It also means that players have to consider a lot of options all the time, characters are unlikely to pick up major new abilities and there is no guarantee that combat numbers or skill rolls within the PC party stay anywhere close to each other.
One interesting variant of this is "abilities on auction" advancement, where the players frequently have the chance to bid some sort of game-related currency on a number of improvements. (See After Sundown). This gives players some control over their customization, while reducing options to a smaller subset. With a random component to reduce self-synergies, this can allow major abilities to be gaining a little more frequently than more point-buy and it can run entertainingly as either a co-operative or competitive minigame depending on the playgroup. However it is still very likely for characters to have abilities which diverge to an unacceptable degree with this variant.
In what I am calling
Hybrid Advancement characters have both some abilities pegged to their level and some abilities they can get with points. Sometimes levels give you packages of points to spend on various abilities, as is the case with 3rd ed D&D skill points and most editions of D&D spellcasting, as well as just about everything in 2e Rolemaster. Other times the amount of points you have spent increases your level, as was the case in at least 1e Mutants and Masterminds. Other times, there's a point-tax meta-variable serving as a soft or hard cap on other abilities (1st ed V:tM's Generation). Any of these can work to combine the better parts of point-based and level-based advancement, such as giving characters in level-based systems more flexibility and customization than would otherwise be available or to provide a way for characters in point based systems to stay within a similar range of power for the key parts of the game, Alas, any of these can also be implemented so as to combine the worst of the previous setups - you can end up with games where: level is easily rendered meaningless as a benchmark (PL in M&M 1e); where point treadmills mean players are likely to lose their characters if they customize them in any but one way (HERO Dex and Spd); where players have too many options to consider each level (Vancian Spellcasting), and other issues.
In
No Improvement advancement, characters are static. Everway, Baron Munchhausen and in practice, any game run as a single shot (which means most games at Conventions ) work this way. It's not terribly popular as it doesn't provide Pavlovian conditioning and the sense of accomplishment for players that having advancement in an RPG does - but it sure is easy to write and simulates a large amount of serial fiction.
In
Treasure Based advancement, the characters' innate abilities do not (generally) increase, but they gain new items with interesting abilities. This can be finding a +N sword in a D&D game, getting outfitted with a boomerang bow tie and poison pellet pen before leaving on a spy mission, or just learning secrets that let you blackmail various NPCs. This is frequently used a a secondary advancement system in level-based, hyrbid or otherwise "no-advancement" games. In D&D (especially 3rd ed and later), characters usually gain new and better items more frequently than they gain levels, and even relatively static characters will sometimes use a weapon or item taken from a prior foe to defeat the current one (see: the Batcave)
In
MC Fiat advancement, characters gain abilities whenever the MC says they do, and there are no further rules for it. The big advantage here is that this is really easy. The big downside is that this is completely arbitrary and players can end up with less control than they want over their characters.
There are a few others out there, Amber Diceless's secret advancement within player specified parameters,
lifepath advancement (Mekton Zeta, Traveller 1st ed), and I seem to recall seeing an even more detailed version where in addition to lifepath training, a character had to devote X amount of their weekly schedule to maintaining proficiencies - but such things are rare and kind of out-of-fashion in RPGs anymore, as well as potentially a subset of one of the above schemes.
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