I'll give this a go. I won't be super elaborate, as this answer by Fizz (that Jhnfui linked in the comments) covers a good chunk in detail. And, for what it's worth, the folks over at Smogon have been doing this a long time, so they're also excellent people to ask.
But for a basic breakdown, I'll try to explain this the way I understand it. The major differences boils down to the stat spread and EV spread of the Pokemon forming the team cores.
- This style is characterized by slower, bulkier Pokemon relying on set-up to dominate the opposition. Pokemon with good defenses which can become wallbreakers after a few turns of set-up fall into this category.
- These teams are slower, and often need some form of speed control (Sticky Web, and the like).
- There's lesser switching around, as they're susceptible to % based entry hazard damage
- They are worn down by Toxic, Sand, and other forms of passive damage.
- Substitute + Set-up is a common set on the Pokemon here.
- EV Spreads focus on HP more than Speed.
- Seen typically around mid-ladder, takes skill to pull off effectively
- A great example would be Life Orb Calm Mind Magic Guard Clefable. Another example would be Rock Polish Weakness Policy Rhyperior or even Shell Smash Blastoise.
- This play style relies on faster, frailer Pokemon who can hit hard, and overwhelm your opponent before they can set-up their win conditions.
- There is a great deal of importance given to momentum, so U-turn, Volt Switch, and Flip Turn are commonly seen on these teams.
- The common EV Spreads are 252 Speed and 252 in Attack or Special attack, whichever that Pokemon is better at.
- Sweepers and Wallbreakers are aplenty in this style, and there's very few Pokemon that are used for utility, usually no more than 1 to either set up hazards or Defog them away.
- Choiced sets are a lot more common than in the previous style
- These Pokemon are quite frail and susceptible to scarfed Revenge killers, and can be shut down by Stall if not careful.
- A common way to deal with opposing defensive walls is by means of Taunt
- Very common in lower ladders, as it's easier to click buttons and watch unprepared opposition go boom
- Good examples would be glass cannons such as Banded Darmanitran, Specs Gengar/Dragapult and so on.
- Most common play style in higher ladders; most difficult to pull off, needs knowledge of offensive and defensive cores, and an ability to balance both offense and defense. Too much of one and the team might fall apart.
- Centered around offensive and defensive cores and relies on synergy between the various Pokemon. Usually contains at least one offensive and one defensive core.
- As the name suggests, there's an even number of Pokemon which play various roles. There are dedicated Sweepers/wallbreakers, Walls/Sponges, Hazard control/Defoggers, Tanks and so on. Not every team contains all of these, but there's good diversity in the sets and EV spreads compared to cookie cutter 252/252/4 sets.
- Relies on timely use and reuse of entry hazards, and is adaptable to opposing teams to create new win conditions as required.
- Defensive pivoting and prediction are very important tools to keep the momentum going.
- Examples are some the common teams seen in the current Gen 8 meta: [Clefable/Dragapult/Mandibuzz/Zeraora/Toxapex/ Single Style Urshifu] or [Volcarona/Rotom-H/Hippowdon/Excadrill/ Single Strike Urshifu/ Rillaboom] or any other such a build.
This is my interpretation of the play styles. Any mistakes I've made in ignorance I'll be happy to edit in if you comment down below. Thanks!