I'm not sure we could list all the different types of Horrors, as they are numerous. Some general categories, however, might be helpful.
First are Horror Constructs. These are life forms either created, or altered, by a Horror to suit a specific need. In most cases, this is a type of feeding (despair, terror, revulsion, etc.). In some, they are simply the minions the Horror unleashes to achieve more physical goals.
Minor Horrors are minor not in power, but in goals. These often can devastate a region, but are satisfied with such small locales as a single town or village or a specific region. Crystal entities, for example, take up shop inside a building or structure, altering it to resemble a brilliant crystalline version of the locale and then terrorizing the locals.
Major or Named Horrors tend to not think so small, even if their power level is relatively low ("low" in this case being something a group of Journeyman adepts could defeat, or an experienced shadowrunning team). These being think in terms of "the big picture" and use their powers to maximum advantage. Nebis is a good example of this (NebisNebisNEBIS). He is frail compared to other Named Horrors, but his goal is the corruption and destruction of the sanity of all peoples. Nebis is an exception, though, as most major or Named Horrors have vast amounts of power, beyond the likes of even an experienced group of adepts or the best group of Prime Runners Shadowrun has to offer. Even great dragons are prey to some of these beings.
Some Horrors exist solely on one plane or another: the astral or the physical. The purely physical ones tend to be more brutish, but that is a generalization since there are several major Horrors that are purely physical that are as skilled in planning and manipulation as any dragon (or great, for that matter). Nemesis, who created a special academy to train adepts and corrupt them to produce an army loyal to itself is an example of this "type."
Some Horrors exist soley on the astral plane. These beings affect the world indirectly: they can only mark and affect things on the physical plane through specific means. They are, however, extraordinarily dangerous as ONLY adepts capable of either entering or affecting the astral can directly combat them. This makes them virtually untouchable, as these beings are quite aware of their advantage and exploit it to the utmost. Examples include Aazvaat Many Eyes, who curses victims through Horror Marked items and slowly drives them insane, or Chantrel's Horror (named after the Troubador Chantrel, with whom this Horror is most closely associated), who doesen't attack the victim it has marked, but it's friends and loved ones. Chantrel's Horror uses those memories of loss and the horror of knowing that the victim brought death to her loved ones and turns the volume up to 11.
And lastly, for this post, are the Horrors that exist as both astral and physical entities. These beings have two bodies, and killing one only inconveniences the Horror. The body that survives can create, or birth or whatever, another version of itself into the other plane. Their astral and physical forms don't even have to be near each other. Thus killing one only ensure that the entity will be more cautious in dealing with its "killers" the next time. Sometimes, it uses its "death" to mark the victims and torment them later, at its leisure. NebisNebisNEBIS, mentioned earlier, is of this type and pulls this trick often.
Does that help, Morg?