thompson wireless router

[#1]

hi i am new to plusnet and not very tech mineded ! so can anyone tell me why on my laptop the connection icon at the bottom of page indicates i am on - plusnet but on my desktop it says network 3 public access ( OR SOMTHING LIKE THAT)  is this normal and safe as both using same router although desktop is using the earthnet cable.  would appreciate help in understanding this. thanks

[#2]

Have a look at  control Panel> network connections for the desktop, see if 3 network is shown as this is the one it is using.
You can r/click and rename it to plusnet.
There can be other connections in there for dialup/mobile broadband/ethernet cable/ wireless card, according to what has been used in the past.