Sterile culture means they are killing all of the microbiology in a substrate, such as
wood chips or saw dust. Non-sterile culture means that they aren't. For example, when I make a Wine cap patch out in my
yard, it is in the yard, It is not sterile. Wine caps need an interaction of bacteria and their own microbiology to produce mushrooms, it is generally believed. The same is true of blewits, for example. When I grow oysters in wood chips in buckets, I cook the chips to about 160 degrees. That doesn't kill all of the "germs". It just gives an advantage to the microbiology that I want, in this case mycelium of oyster. You get more production of mushroom out of the same substrate when it is not cooked at as high of a termperature, and some of the remainder is helpful.
In sterile culture, you use a pressure cooker of some kind, gloves, often agar, and you start in an enclosed dish and have it grow up, usually with a specific grow room.
John S
PDX OR