If a dragon can breathe fire once every three rounds that's a tracking system.
If a dragon can breathe fire in any round that they roll a 1-3 on a six-sided die, that's a reliability system.
If a spell puts someone out of the fight for 4 rounds, that's a tracking system.
If a spell puts someone out of the fight every round until they save, that's a reliability system.
Depending what you're trying to do, there are good reasons to use either one. Tracking systems and reliability systems often appear side-by-side in the same games, used for different things.
Money in traditional D&D is on a tracking system: you get gold you write down how much, you get mugged by kobolds and lose some you subtract it, you buy a horse you subtract some more, you write down the ups and downs of your bank account, you track it.
This makes sense in especially low-level D&D where the adventure is meant to be the drama of scrambling for resources in an attempt to build up from zero to hero (or at least to Scary Person W/ Expensive Armor). The accumulation of resources is part of the main drama of the early game.
Money in Marvel Super-Heroes (aka FASERIP) is on a reliability system--your character gets a Resources stat at character generation and when you try to buy something you roll that stat vs the item's price stat and see if you can afford it that day.
This makes sense in a genre where the main drama is not the accumulation of resources but rather the idea is that you have this person going along living a non-adventurous life until trouble occurs, and the adventures you go on are interruptions to-, and not necessarily related to-, the business of collecting resources in your daily life. The skrulls might attack on payday, they might attack when you were broke.
In the original DC Heroes game by Mayfair, gadgets had "charges"--like Batman's sleeping gas capsules might have 3 charges, meaning he could use them 3 times per day. This meant if you were playing Batman you had to keep track of a lot of things.
In the 2nd edition of DC Heroes they changed it so gadgets instead had "reliability numbers"--if you rolled below a certain number when using a given gadget, it was jammed or out of ammo and you couldn't use it again until you addressed the situation. A bad reliability result on Batman's sleeping-gas capsules would indicate he hadn't packed them that day (and instead presumably packed something else), or they'd gone stale from not being used, etc. A bad reliability result on a gun would mean it was literally out of ammunition or had jammed (important for the GM to decide which in this game, but presumably in a more gun-heavy genre than super-heroes the mechanic itself would specify which).
This 2nd edition mechanic combined the use of a reliability system with another mechanic, whereby the "reliability roll" was actually just part of the normal to-hit roll associated with the thing.
A get-out-of-jail-free card is a tracking system. You have the ability to escape a given danger or you don't, you know in advance, you can use it a known number of times (one per card).
A saving throw is a reliability system. You don't know how many times it'll work or even whether it'll work, you just know the odds that it'll work.
Traditional (non-RPG) card games almost always involve an element of tracking but can also involve reliability.
Traditional (non-RPG) dice games almost always involve an element of reliability but dice can also be used for tracking.
Tracking systems often, but not always, involve a species of resource management (for an example where they don't: it's debatable whether it's helpful to call the dragon's-breath example above a kind of "resource management").
Vancian magic (a spell can be used x times per day) is a tracking system and you can see why many people prefer it to a reliability system. Being limited in how many times a day you can cast a thing can be annoying but in many circumstances it's less annoying than the reliability-system version: taking your wizard's turn to cast a spell and then it does nothing (this may be why so many early edition spells have no save or a save that only limits the effect: the magic-user at least gets to use their turn to do something).
A wizard on a Vancian system who is out of spells at least knows they're out of spells and can start thinking what to do in any given round from there rather than taking turns all about failing over and over.
There are lots of reasons to use one or the other kind of system in a given situation, but that would require making the article longer than most peoples' attention span, so I'll stop there for now.
The main thing is: if tracking something in a game gets annoying, you might want to switch to a reliability system, and if a reliability system gets annoying, you might want to switch to a tracking system.