public ip is something that people on internet will see as your ip address
private ip is something that will be visible in your intranet and not on internet.
you can see both the ip address here
With a few assumptions/exceptions:
1) Routers also run and OS and software which can contain vulnerabilities or for which vulnerabilities may be discovered. Check your vendor (the manufacturer or third party as applicable) for updates regularly.
2) Physical access.
3) Wireless.
4) Mobile devices or laptops on your network.
5) etc (I'm sure there are more but you get the picture. Your home router is only one amongst many things that should be protecting you or your systems).
No. Router != Firewall. In the "real" world routers "route" traffic from the internet to other devices there is nothing that dictates that the devices "inside" the router have only private IPs (i.e.: a router doesn't have to be a NAT device or have NATing enabled). Think of the company you work for or school you attend. It is likely that their outter most connection to the internet is a router "inside" of which is likely a bunch of public devices like a mail server, web server, etc.Said in another way : NMAP scans are useless, in the "real" world, as long as you have a router in front.
I'm a compulsive post editor, you might wanna wait until my post has been online for 5-10 mins before quoting it as it will likely change.
I know I seem harsh in some of my replies. SORRY! But if you're doing something illegal or posting something that seems to be obvious BS I'm going to call you on it.
public ip is something that people on internet will see as your ip address
private ip is something that will be visible in your intranet and not on internet.
you can see both the ip address here