Individual bailout is you carrying everything that you need to get you out of wherever you are at provided you have a total CCR failure. Basically treat gas planning as if you were solo.
Team bailout is anything less than that. It may be enough gas to get 1 diver out from a catastrophic loop failure, or anything in between that and total self sufficient gas planning. In a team of 2, it is usually enough to get 1.5x divers out, and in a team of more than 2, it is enough to get 2 divers out.
A thought experiment concerning “team bailout” when diving CCR in a cave…
Setting Limits for cave diving: How much bailout gas should a CCR cave diver carry… and where?
Bailout Strategies
Rebreather Bailout Gas Management | IntoThePlanet
Whether you're doing individual bailout or team bailout, if you take a CO2 hit you're going to use a lot more gas than normal. In that regard, a team bailout approach should be based on at least 2x the normal gas needed to exit, not 1.5. However, once you're talking a team bailout of 2x the gas a diver needs to exit, and you're talking about it in the context of a 2 person team, you're really playing with semantics - unless you also consider the other aspects of a team approach.
The definition of individual bailout above basically says "enough gas to get yourself out assuming you were solo", but the point Andrew's write up makes is that this can be a lot more gas than you'd think. What Andrew doesn't say is that some of his issues (navigation errors, a flubbed gas switch, etc) could have been mitigated in a 2 person team.
A major question with an individual bailout approach is whether you are willing/able to carry that much gas. The answer to that question for me is usually "probably not", particularly in sidemount dives where the whole point is often to be able to get into smaller passage (where the penetration distance past the last staged bailout is still effectively limited by the bailout you actually have on you). Consequently, I end up doing one or more set up dives to place stages every X number of feet, where "X" varies based on depth, flow, and other actual or expected conditions, such as restrictions, use of a scooter, etc. It's also based on an assumption that a diver who has bailed out will be using 2x the normal amount of gas. Arguably, after a CO2 hit, the actual use may be higher initially, perhaps as much as 4 times the normal rate, but if the diver can't get it back under control during, for example, a 45 minute exit, he or she will probably suffer a cardiac event before they actually run out of gas. There's a point where too much gas won't help and just needlessly increases the logistics, time and deco obligation to get it in place.
In practice, since we dive in a team of two, we place staged bailout containing 2x the gas needed for any one diver to exit, and we don't go any farther past the last stages that than our individual bailout would safely get us back to the last stage. You could call this "individual" bailout. But in fact it really isn't if one of the divers takes a CO2 hit, or perhaps is just panicked, and is thus using more gas than normal AND his or her team mate also has to bailout.
That kind of planning for dual catastrophic failures on a single dive quickly results in either massive logistics, or just thumbing the dive before you even get wet.
But if it happens, how badly this will potentially screw the team will depend on where the second bailout occurs. It's also mitigated to some extent by ensuring the bailout is spread around a bit to ensure that the last remaining bailout gas isn't left in just one remaining tank as you near the exit, which is part of the Mel Clark take on "team" bailout.
In other words, it's more than just a discussion of bare minimum versus maximum practical gas amounts, because the mistake of underestimating the has required can be present in either approach, and some consideration in best practice in actually accessing the bailout during a dive is worth taking about in the team.
In essence, our preference is to use individual gas amounts, but still take advantage of the benefits of diving and functioning as a team when something goes south.