Difference between "attempt" and "try"

As far as I understand, both "attempt" and "try" describe active measures towards achieving a goal. Words like "aim", "seek" are listed as synonyms, but seem not to indicate active measures.

What is the difference between:

I am trying to fix the car

I tried to fix the car

and

I am attempting to fix the car (sounds unnatural)

I attempted to fix the car

Personally, I think that "attempt" indicates one shot quick look (attempted, but was too much effort) and "try" indicates prolonged efforts (done everything I could)

To my ear (product declaration: British-born wrinkly), your theory is right, there is something pessimistic about "attempting". There is no attempting, Yoda should have said, only the doing or not doing. When Eliot, perhaps echoing the Gita, wrote, "For us there is only the trying; the rest is not our business", to my ear that suggests a sustained moral endeavour.

I agree with you also that "I am attempting to fix the car" sounds a bit off, perhaps because, as above, it suggests that you don't think much of your chances.

Other NS may differ in their perception of the nuances, though.

Any claimed difference between to try and to attempt based on degree of effort, likelihood of success, etc. is spurious. The main differences are...

1: try is about 20 times more common than attempt, as that linked chart shows.

2: try has a greater range of "extended" meanings - you can try/hear a court case, try/sample a delicacy, for example.

3: Where the context involves doing A in order to achieve B, the "possibility of failure" may apply to either A or B. Consider...

3a: I tried rebooting the computer
3b: I tried to reboot the computer
3c: I attempted rebooting the computer
3d: I attempted to reboot the computer

...where 3b and 3d both imply the speaker probably wasn't able to reboot. 3a would normally imply he was able to reboot (it just didn't have the desired effect of fixing the problem). Idiomatically, 3c is an unlikely utterance, and I wouldn't like to say which of the two possible meanings might apply.