log in or log on?

English as a Second Language English Vocabulary, Grammar and Idioms
1

Is that any difference if I use log in or log on?

Please log in to the network. Please log on to the network.
Please log in to the program. Please log on to the program.
Please log in to your laptop. Please log on to your laptop.

Sometimes I’m using on and sometimes in because I don’t know which better.

2

Hi, Attila

I remember that Amy answered this very question. Here is her post:

Logged in without being logged in?