Basically:
OTL (output transformerless) means the tube is driving the HP, not the transformer. This design is great for high impedence phones like Byer 600ohm
Tube Amp with Transformer output (like my WA6SE) uses a driver tube to step up the preamp voltage and then uses a transformer to step up energy levels and is matched to lower impedence phones (like Grado and Denons)
Hybrid typically uses the same driver tube architecture but then has an OpAmp (or discreet transistors) to stpe up output and since it is not transofrmer based an opamp can match high or low impedence phones.
So think of hybrid as a non-dedicated amp that is flexible about low or high impedence, but it usually sacrifices energy (power) to have flexibility and hard to drive phones (HD800, T1, HE5) can rarely be driven from hybrid designs (there are more expensive hybrid designs which mimic speaker amps (Class T, Class D) and can run this cans requiring greater energy levels to drive them.
Some people pick and amp and HP combo with these things in mind so they may decide they want to have Denon D7000 cans and from there they have narrowed down their field to Hybrid or Tube amps with transofrmers as the OTL design does not work well with low impedence phones that require energy (I or current=milliwatts) to drive them, not voltage to act as the "pusher" of the drivers, as the high impendence ones do.
Now there are exceptions and certainly more detail to what I tried to paint for you. Some phones are high impendence and also hard to drive so they require higher voltages and higher energy (current) to drive them. Some are low impedence and also are not very efficient (HE5) and these require a high current solution which is one reason head-direct made the Ef5 which is a hybrid with more output than the EF2 for driving the low impedence inefficinet HPs.
There is also design considerations within the base architecture of OTL, transformer output, and hybrid which can help provide niche needs. You will see this in the design of the amp as being Class A, Class D, Push pull, Class T voltage swing, and many more including mixing of class and design to have even more hybrids of design within the base classes.
If it were easy and non-diversified, and not very detailed, I do not think Head-fi would be as popular as it is, but there are many designs and needs based on the many phones and amp designs, and many, many more tastes of sound which people enjoy. I am sitting here at my desk and have listened to AKG 702, Grado HF2, and Denon D7000 phones over the past 5 hours while working. I have alsow switched sources from PC digital music with optical out to Audio-GD NFB-2 to WA6SE, to my TT with RSA F117 Nighthawk to WA6SE. The HF2s I like with digital music but I like the D7000 with my TT as the dynamics are amazing with the closed cans but with the AKG and Grados it is a bit grainy and thin sounding.
So, I hope this helps, please realize this is how "I" understand the difference between amps and how some drive phones with voltage and others with current, and others are a combination, but in no way should this be considered accurate information by any means. I, like others here, have picked up this knowledge by reading posts and asking questions like you are doing and if there were a unanimous statement on here about blue wires being better to power your amp with, I am sure you would find a percentage of members repeating this all over the forums. As always this is IMHO & YMMV!!!