Typically people use the terms "dots" and "nukes" for spell caster abilities.
Nukes are abilities that do damage all at once. This could be like a warlock's shadowbolt, a mage's frost bolt, a druid's wrath, or a shaman's lava burst. These typically have a somewhat long cast time and do a large amount of damage.
DoTs are Damage over Time abilities. Warlocks are probably the most well known class for using dots (more specifically, affliction spec). Corruption, Bane of Agony, and Unstable Affliction are dots used by affliction warlocks. Each of these deals shadow damage over a certain length of time. The damage is broken up into "ticks" which are usually at 3 second increments.
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Here's a basic example:
Shadowbolt - Deals 900 shadow damage. 1.5 second cast time.
Corruption - Deals 900 shadow damage over 9 seconds.
You cast a shadowbolt. It takes 1.5 seconds to cast. After 1.5 seconds the shadowbolt moves toward the target. When the shadowbolt hits the target, the target takes 900 shadow damage.
You now cast corruption. The target receives the corruption debuff immediately. No damage is done. After 3 seconds, corruption "ticks". Since corruption does 900 damage in 9 seconds, 3 seconds is 1/3 of that time, so 1/3 of that damage. On that first tick, corruption does 300 damage. Another 3 seconds pass, and another 300 damage is done. Another 3 seconds pass, and another 300 damage is done. The corruption debuff is no longer on the target.
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There are a few advantages and disadvantages to dots over nukes. Dots are usually easier to cast. Many dots have instant cast times which means it can be cast while running. If you are unable to attack or must run away, dots allow you to continue dealing damage while interrupted. Putting multiple dots on a target and combining that with nukes can put out a lot of damage at once.
Some drawbacks are that dots are damage-over-TIME. They take time to work. This means if you have 5% health and your enemy has 5% health, a dot probably isn't going to save you. Dots generally do fairly low damage at any given time, so one or two dots may not be very effective in bringing down enemies.
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