Dick Johnson describes "hairlines" as scratches in the die that lead to raised lines on the coin, as opposed to "pinscratches" which are depressed lines on a coin (i.e., light scratches).
However, from my first steps in US numismatics on I was informed that hairlines are rather very light scratches on a coin's surface, generally caused by improper cleaning (slight rubbing of the surface).
In this sense, "pinscratches" and "hairlines" are actually the same.
The only difference that I could see would be one single light scratch being called a "pinscratch", as opposed to many light scratches from cleaning or other forms of rubbing, mostly parallel, but also going into different directions, being "hairlines".
Raised lines, coming from scratches (not cracks!) in the die, are to my knowledge called "die polishing". If it were only one single line / scratch in the die, I'd call it a "defect die".
"Die cracks" are a different phenomenon altogether and don't leave marks on a coin that resemble scratches, neither depressed nor raised.