Singleton field getter/setter doesn't work

I looked up what would be the difference between using Singleton and good ol' GetComponent and there really isn't that much in terms of speed so I just went with Singleton as it's much easier to access. So I changed some of my code that still uses GetComponent to use Singleton to access this one script that is attached to my character. After those changes, I can't seem to set a field that I could normally set before and getting was not working as well. After some testing, I tried to revert back to GetComponent and setting worked again. I'm wondering what could be the reason for this behaviour?

A small side question. Is the long getter/setter(get{ return _something; } equal to the shorter getter/setter(get; set;)?