I think the temperature,altiude and how much moisture is in the air determines how defined the contrail is,the colder it is and the more moisture will make a heavy and long contrail,sometimes up to 50 miles long,large contrails are usually seen in winter and in the summer usually very short wispy ones or none at all.
I think contrails start to form around 25000ft if the conditions are right.
I think the fuzzy one that you are talking about is some sort of optical illusion.maybe someone can give a more detailed explanation.
hope that helps
Regards
Rick