The SIM is the card you put into the handset to associate a mobile phone account with it. If you use it to connect to the Internet then you are probably sending it over the mobile phone provider's frequencies using a system called WAP. Depending on the account you have using the service provider's phone network might prove expensive. Best to use only if you have a large or unlimited 'included data' allowance.
I may be misunderstanding but I've not heard of a broadband dongle SIM. Dongles are things you plug into PCs to do various things. Some will connect you to broadband in which case it is probably using WiFi to connect you to someone else's wireless network. Many will ask you for a password since folk have to pay for their WiFi network, but there are open ones out there.