All-in supports do just what it sounds like. They go ALL-IN. Essentially when they go they GO. There is no brakes or ways to get out. This is why typically
and
are some of the bigger all ins. They don't really have an escape out if they screw up. THere are some that fall into "all-in" without following the same.
fits this model. He CAN go all-in, but he doesn't have to. THe thing that gets him labeled here is again once he decides to go there is no coming out until the fights over. "all-in" supports focus on singling out one target and destroying them as fast as possible. Usually they have pretty heavy CC in either displacements or stuns and as you know, are really tanky.
Other Examples: 
Poke Supports are those that again do what it says. Champs that focus on whittling down the enemies HP bars slowly overtime. Champs like
,
fit this mold. While they have the utility to back them up they focus on damaging the enemy champs. Usually these champs are very squishy and don't really want to fight you unless they have a huge health advantage.
Other Examples:
, 
The other big category is Heal supports. Again name tells exactly what they focus on. Here are the champs like
, 
While these are good broad categories there are actually 3 better categories to describe champs since we are missing disengage, burst, etc kinds of supports. Also these aren't good categories since some champs blend with others.
It sounds like you need a basic understanding of different bot lane comps tho. There are generally 3 different types of bot lane compositions: Sustain, Poke, and KIll. Now most of this (90%) is dictated by the support chosen and really has little to do with the ADC.
I'll start with Kill since those are what you asked first about. These are your All-in champs. The whole goal of this lane is to get a kill. You don't have sustain in most cases and want to harass and trade. Kill lanes also include your burst champs like the
supports. These lanes tend to beat Sustain lanes. They will go in a lot and enough that sustain lanes can't stay healthy.
Good ADC's for this lane:
,
, 
Second is sustain lanes. These lanes focus on just staying alive. This lane tends to be weaker early game or just easily out-traded. So this will have your healing supports to make sure that your ADC can stay alive through the laning phase and become stronger. Normally you don't want to fight until have jungler presence or a roam in general. Sustain lanes have an advantage on Poke lanes since they can survive their poke with sustain.
Poke lanes are the last. This lane focus's on always knocking you down so you can't really do anything else to them. This is where the obvious supports go that I listed above. Poke lanes excel over kill lanes since they can stay back and keep the kill lane supports down and make it extremely risky to go in without jungler help.