Short answer: They are meaningless corporate titles applied to people with similar (apparent) skills. They're the same.
1- How do human factor specialists and user experience designers differ?
It all depends on what definitions you ultimately settle on. I have held both titles of "Human Factors [something]" and "User Experience [something]", my knowledge and skill set didn't suddenly change when I moved from one to the other.
I've found that "User Experience" is the latest buzz title for usability professionals who generally apply their knowledge to software over more physical applications, with those individuals more commonly being referred to with a "Human Factors" title.
For the sake of the "UX versus Human Factors" argument I will use the idea that UX is more software oriented and Human Factors is more hardware/physical/ergonomics oriented.
If you go to UX is Not UI you will see a good example of how "UX" is contrasted with the software interface, but look at the UX side. Almost every bullet can be applied to Human Factors...
When holding a "Human Factors" title, I touched every one of the bullets in the "UX" column for a hardware system. The language used in the "UX" list is very software driven, but any bullet you point to as software centric can easily be adjusted to line up with hardware system.
The one aspect of UX that has traditionally not been included in a definition of Human Factors is the "enjoyment" of the system. Human Factors (traditionally) is defined around making a system usable -- no matter if you "enjoy" working with the end result or not. A short article on The Definition of User Experience at the N/N Group has the following line:
Next comes simplicity and elegance that produce products that are a joy to own, a joy to use.
This is not to say that someone with a "Human Factors" title isn't going to make something enjoyable to use. The "common" definitions of the fields simply differ with the addition of a strong focus on enjoyability.
2- How does this apply when it comes to designing for other real life situations for example in avionics?
I worked for a major aviation manufacturer for over 8 years. During that time my title always had "Human Factors" in it. In addition to work with cockpit ergonomics and design, I worked on software systems that would were destined to be used either up in the air or on the ground. I never had to change my title.
The company does have people with "User Experience" titles, which I discovered only after leaving. These people were focused on consumer software products (support and maintenance mostly), while people who worked on the planes (targeting software or hardware) tended to hold "Human Factors" titles.
3- If UX and human factor specialists don't different that much.
"User Experience" and "Human Factors" only differ to the degree of the definitions you apply to them.
My opinion, hopefully illustrated above, is that they are basically the same. The general public consciousness (in my opinion) tends towards "User Experience" being more software oriented and with a (apparent consumer oriented) "enjoyability" twist.
has anyone came across a situation where user experience skills were utilized within the aviation industry?
Yes; every day for a little over 8 years. My leaving the company didn't change that there are still dozens of very talented people still applying those same skills in the same context.