It is idiomatic, alluding to reading a meter for the quantity being measured. Imagine there was a gauge like a fuel gauge in a car that measured the number of job vacancies, and the gauge included a shaded area where there were the "right" number of job vacancies. "On the low side" would suggest that the gauge is at, or slightly below, the shaded area. There is an acceptable range, which has two sides, and the quantity is at the low side. It implies that there are fewer that would be desirable, but not necessarily too few.
"On the high side" can be used similarly to mean that there are more of something than would be desirable, but not so much as to be dangerous or incorrect.
Strictly, no. The meanings differ.
In very informal speech you are almost always going to be understood to mean the same thing in either case.
But there are cases in which you might want to take care.
Still in English (if not universally) there are simple rules that can help you decide when you should be careful.
When you
use a figure of speech--an expression
and
your topic relates to one of the content words in your intended figure of speech
you need to consider what your listeners will understand.
You do risk not being understood at all or being understood to have said something much different than you meant.
For instance, you might hope to be a martyr for some cause. However you should not use either of these expressions in this context. They involve killing and dying so your listeners could easily become confused.
You can't reasonably say anything like the following:
I would die to be a martyr for [anything that you say here is wrong].
I and my gang would kill to have the contract on his life.
You could say:
After three years abroad I would kill for a decent milkshake.
I am dying to get my hands on a new car. The daily walk to the office is killing me.
Why specifically?
To choose to die for something is to be a martyr. The statement is illogical.
A contract for someone's life is a promise of money in exchange for a killing. Here the statement isn't illogical.
It is possible that you could become a paid killer if you had
already killed someone. But you can't say it this way. You might sound as if you were making a joke--or maybe what you mean is unclear.
It's confusing for anyone listening. So [assuming it is what you mean] it would be best to say
We would be willing to murder someone to get that contract.
Those are extreme examples but when your meaning is even potentially related you can have the same problem.
You can say I would kill for a beer now but you can't say I would kill for a friend if you mean I would like to have a friend.
Likewise I'd die for a beer now is perfect English. But in a hostage crisis don't say I'd die for a friend now.
Best Answer
This could probably be answered from a dictionary, however, here is an answer.
A 'threshold' was in origin the border or edge marking the entry point to a house. When you enter a house you 'cross the threshold' as you pass the door.
So, by transference, 'threshold' has come to mean 'the point at which something changes from one state to another'.
So, in your example, someone with Anti-Social Personality Disorder will not be scared in circumstances where 'normal' people would be fearful. Nevertheless, there is a point - a threshold - after which even they will be scared.
A 'high' threshold means a person or thing will only pass to that other state (eg being scared) later than the norm. A 'low' threshold means a person will pass to the other state earlier than the norm.