If I am trying to do a sudoku, and you let me know that my hair is on fire, is that a distraction? It seems to fully qualify as a notification, a term with special meaning on tablets, phones and computers these days. You have notified me about the condition of my hair. If I didn't hear you, I guess it is a failed notification since I am not notified. We seem to get back to the old intangible of intent again. When I stop working on my puzzle and douse my hair, I could be said to have been distracted from my puzzle. If my concentration is so intense that I hear you and even respond but continue working on my puzzle, maybe I didn't really process the meaning of your notification even if I said, "Thanks for the warning."
If I am rabbit hunting and I notice that I am being stalked by a tiger, I may forego my hunting in favor of barricading myself in the bathroom or switching guns to my larger bore gun. When I get a notification, I have to make a quick assessment of the relative value of continuing with what I am doing or switching to something new. The apps on my iPad include many that represent commercial interests and they usually want to notify of every damned thing, every sale, every deal and more. So, I prevent notifications from them appearing in the midst of other screens. I dislike looking at an article online and having something pop up blocking what I am trying to read with a message of a different product or show. Using the browser Firefox, I have a little icon in the URL (site address window) that very nicely blocks everything except the main story on that page. I have read in the Tips on my iPad that the official Apple browser, Safari, has a similar feature but I have never used it.
This same notification, assessment, take up distraction or continue with previous activity sequence happens all over. My body itself has the sequence built in. Get a serious pain and go to the emergency room or ignore it and keep jogging or whatever. Reading warnings and other notifications and deciding what to do about the new information just delivered is all over our lives. When the government wants to notify me of jury duty or a tax due, it sends something in the US mail. When they are really serious, they require the mailman to get a signature that says I got the notification and I acknowledge getting it.
I can tell my secretary to hold my calls and not to distract or interrupt me but he may ignore that if the building is on fire or I am late for an important meeting. We are juggling, concentrating, being notified, being distracted, concentrating, switching activities all the time.