Autism and ADHD

Hi everyone. I received a high functioning autism diagnosis just over a year ago (at the age of 36) and have been dealing with understanding it ever since. 

I have been having regular sessions with a clinical psychologist at my local mental health hospital as as well as the diagnosis I was also told I was suffering from depression and anxiety. 

A large part of our chats revolve around my concerns about getting back into employment. She has mentioned, as have I read online so many times, that employers love people on the spectrum who have crazy attention to detail. 

This is when I feel like a fraud. I make stupid mistakes all the time, I lose focus on longer tasks and flip flop between interests. In my previous jobs I was able to do really technically complicated things like software development but made silly errors and was unable to do simple data entry into a spreadsheet. This theme has followed me since primary school. 

Today I accidentally came across an article saying that it is common for people on the spectrum to also suffer from ADHD and it then listed the common symptoms of ADHD. I tick an awful lot of them. 

What I don't understand is how can someone on the spectrum, who are supposed to have incredible attention to detail, also have something like ADHD where they continually make silly careless mistakes - I don't see how they are compatible. 

I'm going to raise this next week at my next session - it very complicated as I am, as far as the diagnostician and the clinical psychologist I've been seeing, autistic. But as I say, I often feel like a fraud and before I start looking for a job openly stating that I'm autistic, only to say "oh, but I don't have some of the really useful attributes",  I want to make sure I fully understand it. 

Does that make sense? Any thoughts?