They definitely can have something to do with each other. Anxiety and Depression linked to ADHD is a very common symptom and it's typical for patients who suffer from undiagnosed ADHD to seek medical assistance for the first two and then being diagnosed. Anxiety and depression can often be a co-morbidity (I hope I use the word right) of ADHD.

For me personally ADHD gives me anxiety due to the feelings of stress it causes and the depression comes from feeling unable to handle/cope with it.

I'm not a doctor but I do have adhd, depression and anxiety. A quick Google confirms they are in fact linked, so I'm not sure what you mean by "have nothing to do with each other".