Relationship between a recovery and a ROM As far as I understand: 

Recoveries (e.g. ClockworkMod) can be used, among other things, to install new versions of the Android OS, like custom ROMs (e.g. CyanogenMod) by updating the ROM section which contains the Android OS firmware. Recoveries are entered by shutting down the phone and powering it up by pressing special button combinations, so the phone doesn't enter the regular OS, but instead activates the recovery section.

Now, from that I expect that, the Recovery is something like the boot system on a PC (e.g. GRUB), that is separate from the actual OS, and activated when there is trouble getting into the OS. And because it's not a part of the OS, it can be used to update the OS itself.

However, what I'm confused about is this: 


The guide to installing CyanogenMod on GT-S5570 says that "The official Android 2.3 update from Samsung must be applied before following this guide." 
Another guide for flashing the ClockworkMod recovery on GT-S5570 also says that if you have 2.2 on the phone, you have to use a different version of ClockworkMod recovery, than if you have 2.3.


What is the relationship between these two, a recovery and the Android OS?

Further: 


Is a different version of the recovery really needed for different OS versions? 
Is this something specific to ClockworkMod, or is it how Android's recovery system works always? 
If a recovery can be used to update the OS to a different version, does the recovery then become invalid after the update?
Is a different version of the Recovery really needed for different OS versions?


No. In case of updating custom ROMs you're completely right in that the recovery is mostly* independent of the ROM used.
However, phone manufacturers sometimes push out updates that change some vital parts of the phone. For example, repartition the phone. This is why sometimes you need a different recovery for the phone after major software updates.


  Is this something specific to ClockworkMod, or is it how Android's recovery system works always?


This is something that depends on the phone and the the manufacturer's customizations.


  If a recovery can be used to update the OS to a different version, does the recovery then become invalid after the update?


Factory ROMs are not always in the update.zip format, thus they're not always applied using the recovery. In these cases, the recovery is commonly among the parts that are updated. Furthermore recovery can be updated from the recovery just like the boot image (kernel.)