There are two types of licenses: Node-Locked license and Floating License.
For one single node-locked license, you can not use it on both machines, so you can either use it in school or at home, but it is perpetual, not internet access required.
The floating license on the other side, you can use it anywhere with an internet connection, but it is not perpetual, usually, it is a monthly or yearly subscription.
Regarding products, MG-Picker Studio node-locked offer different price for the individual user and a company user. You only need a license when you need to design picker while using a ready-made picker file is free.