You are confused me

, i have few questions -
For my site hosting i use my PC, not 3d party services. My machine is connected to internet

, in installation process i set my host to
www.site.x. My databese is setuped to my local machine IP. I managed my site from home machine and from work machine (another LAN, ISP). I also tested my site work from another computers in library and internet cafe. Everything work fine. I use XAMPP webserver and configured my server for virtual hosting also (i have another full working website on my machine too). How i gather from another posts, my installation process was just litle different, like if i use 3d party hosting services. I just unzip installation files directly in my site folder. How i understood In another instances peoples should upload their site by ftp with permision XXX.
1)Could you please make for me clear - why my installation is local, but another one (if i will use 3d party hosting services) are online installation? Only because i instaled site from local machine?
2)If i will make new installation from work computer is it solve the problem?
3)Is this situation with unregistred copy cause for me problems in future?