It's not really a spectrum but a collection of symptoms whereby if one exhibits many or the majority of them in enough frequency, intensity, and duration as to negatively impact their life, one can say to be ADHD.
There are different subtypes (not sure if they are in the DSM but they are often referred to in other literature), e.g. hyperactive vs non-hyperactive. Sometimes, though, the hyperactivity exhibits itself in ways that are non-obvious.
I think the negative stigma comes from what many (myself, included) believe to be an over-diagnosis in young children. It seems to be used as a catch-all for children who are difficult to handle, who aren't good at sitting still in class, etc. This over-diagnosis causes a lot of people to think the disorder isn't real.
Secondly, a lot of people will try to fake their way into an ADHD diagnosis (especially at the college-level) to gain access to the amphetamines. This makes it difficult for those with the actual disorder, as we are scrutinized heavily and often made to feel somewhat criminal when we pick up our prescriptions at pharmacies that have had issues with this in the past. I won't say it's overly common, but it does happen. I've been told they were out of stock before because I tried dropping off a prescription at 3am once. I had it in my wallet and had meant to drop it off on my way out with friends. On my way home, the subway stop I get off at (I live in NYC) is where my 24/7 pharmacy is. I didn't think anything of it, I'm just dropping it off to save myself a trip in the morning.. well, the pharmacist looked at me.. 3am, clearly had a few drinks.. and he gave me the "we're out of stock" line. Magically it was re-stocked at 7am.
And lastly, there is a stigma in the US, in general, when it comes to mental illness. These aren't things people can see, for one. And, perhaps more importantly, our mental selves are what we view as our actual selves, so people can have a hard time admitting to themselves that they have something about their mind that is considered abnormal. Other people have a hard time accepting it because they simply can't relate - how do you explain to someone what it's like to be ADHD?
You might tell them that you forget things a lot, feel impulsive, etc. and they simply say "Yeah, everyone is like that though, you just need some discipline and will power dude." What they fail to recognize is that, yes, everyone does feel that way sometimes. Just like everyone feels anxious sometimes. What makes it a disorder is the frequency, intensity, and duration of the feeling(s). Many people just can't accept this, especially in the US it appears. Our attitude is "pick yourself up by the bootstraps" or "be a man" or "put yourself together - no one's gonna do it for you. I certainly didn't need medication!" and there's a lack of empathy because they simply can't understand.