Now this is something that I've noticed throughout my career in WoW as a healer. When you, as a healer are assigned to a specific tank over a long period of time, you become attached to each other. You begin to talk to that person more readily and regularly, and you have a certain type of relationship that allows you to play together as you do.
The Playful Tank/Healer.
This is a combo you don't see often as many a healer isn't assigned to one specific tank long enough for the relationship to advance this far. This is a relationship in which the tank and his/her respective healers joke about letting the other die, or dpsing when they are supposed to do something else. You get sarcastic remarks flung back and forth with these two, but it is always in fun. In these cases, the two involved are either social and thus the relationship advanced faster or have been playing together long enough to know each other and how they play. This team is usually your best healer/tank skill wise, though sometimes this is not the case.
The Serious Tank/Healer.
This combo is one that many people hate having. With this team, either the tank or the healer, or both is very serious about what they do and almost never do anything else. With this team the relationship is less social and more like a business, with one or both of the people trying to min/max the other and make sure they are performing to the best of their abilities. With this team, it is likely two players that do not participate in the guild as much as others and feel that they are not up to par with the rest of the guild.
The Disconnect Tank/Healer.
As the name implies, these two individuals have a disconnect between raiding as a tank/healer team, and just being in the same guild. With this combo, the two respective tank/healers don't interact that much with each other outside of raids. Now, in raids, these two perform well together and actively try and make the others job easier. This is also a team that will be very social, but polite with each other, as they do not have a strong relationship.
These are only the basic combo's that I've encountered, and there are many people that can't be dropped into these categories. Many people fall in between Playful and Serious, with some being at the extremes and others not. As long as your tanks and healers can work together though, they are doing their jobs.
-Brought to you by *HEROISM!* "Look at me! I'm casting so fast it's like I'm on roids or meth but really I'm just fucking huge and really goddamn fast!"