The main difference is that NAT SHARES the IP address with your host which can make things easier if for example you need to connect to a wi-fi configuration that only has a limited number of IP addresses available such as University "Dorms" or "Halls of residence".
If your LAN addresses are say 192.01.x.x your NAT VM will have an address of maybe 10.0.0.1 or whatever (an Internally automatically assigned address) but any Internet request from your VM will be sent out as having an IP address of your HOST machine (192.01.x.x). This makes running things like RDP to your VM from outside your network very difficult if not impossible.
Bridged gives the VM a totally separate IP address on you main network such as if you have a router at home where your network addressses start at 192.01.x.x the IP address of your VM will also be in the range 192,01.x.x. You can use this for example to RDP to the VM from outside your internal LAN.
Probably as "clear as mud" but hopefully some help for you.