There are 3 different types of ADHD and some people have only one type, others have multiple types. Personally, I have a little bit of all of them.

My thoughts vary in style when I'm off my meds. When I'm hyper focused, I do sometimes focus extremely intently on the thing in front of me and can't think of anything else like what some of the people above me described. But that typically only happens when I'm very interested in the topic at hand and wide awake. Much more often than that, I struggle with the opposite issue and can't keep my mind in one place. I move through topics rapidly but it isn't like I'm having random thoughts. All of the thoughts are inspired by the environment and the only time they are not is when the are intrusive thoughts caused by my PTSD, not ADHD. It's almost never remembering a scene from a movie or something like that completely in a vacuum. If I did think about a movie scene, it would be because something around me reminded me of the scene or something around me made me think about something else that reminded me of the scene. If I were to start talking about my thoughts aloud to someone else in the middle of the thought, it would sound random to someone else, but in reality they are very linear. I just move through the line quickly. It's never like the stereotypical "ooo squirrel" randomness like we're so frequently portrayed in the media.

That particular type of thinking is similar to what you described and falls under the category of impulsive type. However, thought patterns like this also happens in bipolar disorder as well as sometimes anxiety disorders so it is important to get an evaluation done.