There was a heroin addict who filmed himself going cold turkey for his family, and at the end of the video, was himself on camera, having a brain hemorrhage.
You're right that it's very extremely different than caffeine but a brain hemorrhage? That's not typical of opiate withdrawal at all. In fact, even in the most severe cases of opiate addiction, the withdrawal itself is rarely life threatening. Very rarely life threatening. The drug class that does have a potentially fatal withdrawal syndrome is the benzodiazepines (anxiety meds like Xanax and I'm not sure if alcohol is in that same class but it has the same withdrawal syndrome). The danger with those are fatal seizures most of the time. But opiate withdrawal can't kill you unless there are other underlying conditions or something. I say this because drug education in the U.S. is awful and most people only know the misinformation they were taught in school and get the wrong idea from something like what you mentioned, a video where the guy has a hemmorage at the end which was most likely unrelated to opiates.
That said, all addiction is very similar. I would say that people more often than not really mean dependence rather than addiction when it comes to caffiene but the problem is that most people think of those terms as being the same thing. They're not. Dependence can exist separately of addiction but addiction will always go together with dependence. Dependence is (very simplified here for brevity) when your body relies on a substance from outside itself to function normally. Usually that's because you've put a substance in for so long that your brain downregulates certain chemicals because you're replacing what's already there with something from the outside. Take the substance away and it takes a bit for the body to realize you won't be putting in any more nicotine or caffiene or opiates so it takes a while before it starts producing enough acetylcholine or adrenaline or endorphins or whatever the case may be. Addiction is dependence plus a certain set of behaviors (again, trying to be brief and simple here). A caffeiene "addict" (read: dependant) isn't going to rob the local Starbucks to get a fix like a true addict would. You don't see these caffeine addicts ruining their lives because their persuit of coffee is interfering with their jobs or their marriage and such.
There's a big difference not only between the withdrawal syndromes but I also think an important point is to stop thinking of these people with such stories as addicts. They're probably just dependent. A guy who gets sick if he stops taking his antidepressants is dependent. A guy who can't stop himself from downing medication X and puts his persuit of substance X above all else with serious negative consequences in other areas of his life is an addict.
Opiate withdrawal can be extremely unpleasant, but the direct health risks are very low. Things like methadone exist to make things psychologically easier and reduce the rate of relapse. As mentioned, alcohol withdrawal is actually much more dangerous.
Anecdotal evidence I know, but I was a three cups/day guy for a while then quit cold turkey. After about a week of feeling a bit fuzzy and irritable I was back to normal. Is this atypical or something?
Nope, that's typical. I looked up the data a while back. 1-2 weeks is the general timescale for developing dependence and for withdrawal. Once your neurotransmitters reset, you're pretty much back to normal.
But, yes, drug and alcohol detox units save the beds for alcoholics (who can die during detox) and not for heroin addicts (who tend not to die during detox).
Very unlike caffeine.