When I "became" disabled I had the novel and often frustrating experience of using a wheelchair, then walking frame and finally a walking stick (permanently). I have seen both how differently people treat you depending on how disabled you look and how other differently able bodied people see you within what could be called a disability hierarchy.
I was in a wheelchair for 6 months when I was unable to walk and I was definitely invisible. People would look over my head, pretend I wasn't there and sometimes dramatically sigh if they had to walk around my chair. People would also talk over my head and ask my companion if I would like ..... Hello it's my legs that don't work not my brain and voice! Of course some people were nice, treated me no differently but on the whole I was, maybe unintentionally, made to feel as though I should be grateful, where just a few months previously before my accident I would have taken such interaction for granted.
Other disabled people treated me as one of them as I was obviously disabled - nothing screams disability more than a wheelchair, neck brace and partly shaved head! I was never asked to "prove" my disability when using my blue badge or hospital transport to one of my many appointments!
When I moved on to a walking frame much of the above still occurred, the only difference being that I now had a potential implement in my hands that I could use to mis-manoeuvre into people's ankles if they were dismissive of me, then smile pathetically and croak that "I hadn't got the hang of it yet" I still didn't get asked for "evidence" that I was disabled when using my blue badge/ disability services but I had defiantly moved down the disability hierarchy, hearing muttering that "she can walk" and "she doesn't need as much help as me". I wasn't talked over anymore but people still talked slowly or would sometimes ask my helper to confirm what I had just said.
Finally I have moved onto a walking stick (hence lots of posts about fashionable walking sticks). They are great for tapping people gently out of the way when they expect you to walk around them (I can only walk forwards so it's never going to happen). I have to zig zag down streets yo avoid getting knocked over, which is exhausting and my stick regularly gets kicked by other shoppers invading my personal space! I still get the sympathetic glances and the "but you look normal when you sit down" comments when I have to explain what is wrong with me. I don't get talked over my head anymore .
When using a blue badge / disability services I have been told that I am not disabled enough/ I am too young to need them and they need it more (disability never should be a competition).
This is based on my personal experience and does not aim to be a monologue speaking for all disabled people.