Yes, it's what's known as a spectrum condition, so there are a set of 18 diagnostic criteria across two subtypes. Nine symptoms relating to inattentiveness (if you have five of these, you're considered primarily inattentive) and nine relating to hyperactivity, so if you have five of these you're considered primarily hyperactive. If you have at least five of each, then you're considered combined type.
So two people with the same presentation of ADHD will always have one main symptom in common, but the other four could be totally different. It is thought that there are two main presentations, which is why there are two symptom lists.
Also, the criteria must be occurring more severely and/or significantly more often than in other adults of your gender/culture, and they must be causing impairment (e.g. bad school grades, lost jobs, financial losses, failed relationships, poor parenting, car accidents, trouble with the police, difficulty sticking to medical treatment regime etc etc) in at least 2 areas.
Also, the problems must not be better explained by another disorder. So for example if you're a chronic insomniac and you're always forgetting things, that might not be ADHD, it might just be that you're tired. If you struggle to get out of bed but you're also depressed, it might be the depression. This is why currently it's required to be diagnosed by a psychiatrist.
It is a bit more complicated than this in reality, but this is what the DSM says.
The main thing that's more complicated is that the adult form of the disorder has not been studied as much as the children's form, since it was thought entirely until 1980, and still mostly until around 20 years ago that it was purely a disorder of childhood, and that most children would outgrow it with only a few continuing symptoms of inattention into adulthood. What actually happens in reality is that people with ADHD typically outgrow the childhood symptoms. They still have ADHD, but ADHD in adults looks different to ADHD in children. When it was first included in the adult section of the DSM (edition 3) they just ported over the children's symptoms and changed the wording (e.g. swapping "school" for "work" and rather than "the child is unable to play quietly" it's something like "cannot engage in leisure activities quietly") In childhood, you need at least six symptoms from either list to be diagnosed whereas in more recent DSM editions for adults the criteria is only five, and there's an argument that this ought to be reduced to four in the next DSM version. The problem is that changing the DSM is quite a stringent process understandably, so in order to get something changed you have to prove that it "improves the accuracy of diagnosis to a degree that outweighs the downsides of changing the criteria".
So often the symptoms that you will find adults discussing on internet forums etc will not necessarily align with the ones written down in the DSM. The DSM is just a diagnostic manual, so it's not intended to be a list of the most relevant characteristics, just the characteristics that most often differentiate people with ADHD from the general population. And the adult characteristics are still based on the child criteria, even though adult symptoms typically vary.