Let me break it down a bit more...
A DK has several types of abilities, much like a hunter. You have your stings, your pet, and your shots, and then some shots do other things (like concussive shot, tranq shot, etc), and of course - auto-attack. We have diseases, a ghoul, our strikes, some other utility abilities, and auto-attack. Let's compare them...
Pets:
A hunter's pet is always active, in solo is his tank (unless he is kiting) and in groups is a nice portion of his DPS. While he's a great help to an MM or SV hunter, he's absolutely incredible for a BM hunter. With a DK, your pet is a little different. As a blood or frost DK, you will have your pet up only some of the time. He serves then as either burst damage in instances, or as an "oh sugar" button when you need him to tank for you. As an unholy DK, he becomes a lot more like a pet (albeit sometimes he may not be up if he dies real quick) and he would be a lot more important. As to healing, it's a lot more limitted, because Death Coil really doesn't heal that much, and costs 40 runic power (which takes several GCD's to get).
Diseases are comparable to stings or judgements, in that they are debuffs. Blood plague is simply a DoT, but Frost Fever adds a slowing effect (to melee/ranged attacks, as well as to movement if frost) and the DoT, and Crypt Fever or Ebon Plaguebringer (unholy talents) will increase damage by diseases and spells (they are one disease, as CF turns into EP). While they do some damage on their own, their main purpose is to buff abilities like Scourge Strike, which deal additional damage per disease on the target.
Since diseases and strikes both cost runes, it's actually the combination of 2 (and thus the rotation) that cause damage. For example, as a hunter I'm sure you're familiar with the old 3:2, 1:1, and 1:1.x rotations hunters had? Well, as an unholy DK there's 2 solid DPS rotations, the 1/3 and the 2/2. It can be explained better
here (note that they use Blood Boil because at the time, Reaping did not include Blood Strike). Basically, the numbers refer to how many Scourge Strikes you do in a row. The 1/3 rotation is required to start off the fight (due to conversion of blood runes to death runes), which results in this rotation:
Icy Touch (applies Frost Fever) - Plague Strike (applies Blood Plague) - Scourge Strike - Blood Strike (gets a death rune) - Blood Strike (2nd death rune)
Scourge Strike X3
The 2/2 is then:
Icy Touch (reapply Frost Fever) - Plague Strike (reapply Blood Plague) - Scourge Strike X2
Blood Strike x2 (regain death runes) - Scourge Strike x2.
As you can see, the rotation factors in diseases and strikes. Your pet will be used as a cooldown in Blood/Frost, and as a pet in Unholy, leading you to pretty much swap it in during the spare GCD's (as you can see in the other post, you have 4-5 GCD's to use on RP dumps or cooldowns). On single target fights, you will likely deal most of your damage with those, but on AoE fights you will switch it up for rotations involving 2 diseases, pestilence, blood boil, and talented abilities (such as howling blast, corpse explosion, and unholy blight). So on AoE fights your DPS will come mostly from AoEs (which will eat your runes so you cant do rotations) but on smaller-size fights your DPS will come from strike rotations.
While the rotations above are specific to unholy, a frost DPS can replace SS with oblit, and a blood DPS can oblit then spam heart strike. However, the point was not the rotation itself, but rather the effects it has.
You can also consider our presenses to be similar to aspects, in that they don't change what abilities we can use (like a warrior's stances, druid's forms, or stealth) but rather just how our attributes work. They each have their advantages, and they are actually surprisingly unique from each other (whereas warriors just varried the amount of damage taken and damage given).