All those terms are really muddled and hard to properly define. You can ask 10 people and get 10 different answers. Here's a longwinded explanation of my use of the terms.
In terms of concepts (not decks):
Aggro vs Control (or Beatdown vs Control) are polar opposite roles on the same axis. In every game, each player typically takes one of these roles. The player who is Aggro/beatdown is trying to end the game quickly, and is willing to sacrifice resources like card advantage and his life total to get there quickly. The player who is Control is looking to drag the game out, to eventually win on card advantage / quality. Note that these are roles played in a specific game, and any deck can play either role depending on what it's up against, what it has drawn, etc.
Tempo as a concept generally refers to actions that make your position stronger in the short-medium term. It's related to the concept of card advantage, but instead of giving you +cards relative to your opponent, you're giving yourself +time relative to your opponent. That can be as simple as playing really mana efficient creatures (Chillwind Yeti). It can mean casting Wild Growth in a druid vs. druid matchup, allowing you to get the big stuff out faster. It can be casting Sap on a big enemy minion, thus making him spend 5+ mana to counter your 2 mana effect. You can buff your 2-drop with a Shattered Sun Cleric, using it to take out a 4-drop. In MTG, you could also destroy an enemy's mana for the same effect.
The concepts are generally agreed upon, but when it comes to naming decks, it's a lot more ambiguous. The naming convention I used above is pretty much as follows:
Deck archetypes
- Aggro: Any deck who will play the Aggro role against most decks in the metagame, because that's all it can really do. Doesn't really want to interact with your shit unless it has to.
- Control: Any deck who will play the Control role against most decks in the metagame, because that's all it can really do. Generally tries to kill your shit, gain card advantage and delay the game until it can play one of its few win conditions.
- Mid-range: A deck who takes a very purposeful middle ground between Aggro and Control, aiming to play the Aggro role against Control decks and the Control role against Aggro decks.
As you can see, these three "archetypes" are named for their positions on the Aggro - Control axis. Thus, with any decks lying "in between", it will be very hard to define them.
- Tempo: Used to describe any deck whose core strategy is to exploit Tempo plays, as defined above. Board Control Warlock/Rogue fits the bill, using lots of buffs to make their previously played low cost minions stronger, and using them to take out their opponent's freshly played, more expensive minions. Thus gaining time advantage, and using that time advantage to win the game. Almost all tempo decks are aggressive by nature to exploit the temporary advantage from the tempo play.
Finally, a deck archetype that we in my opinion have only seen one example of in HS thus far (Unleash OTK):
- Combo: A deck that generally doesn't give a shit what you're doing, it just uses all its early turns to build a scenario where it can unload a combination of cards which ends the game instantly. All resources are used to set up that condition, rather than trying to interact with the opponent.
This is all very spergy, and MTG nerds can (and do) spend hours discussing what these terms really mean. I'm sorry.