When you type giveawayoftheday[.]com in the address bar of your browser and press Enter, you don't immediately connect to the GOTD server[s]. Instead, you're connected to a DNS server that looks up that URL and then routes your connection to the IP address 204.155.149.200 . Normally you're set up to use either a DNS server provided by your ISP, or one of the free DNS servers provided by companies like Google. SmartDNS provides a paid DNS server that acts as a proxy by changing your IP address, so that any site you connect to thinks that you're in a different country. That bypasses restrictions if/when the site you connect to is not normally available where you live. The advantage is that you keep whatever bandwidth you have from your service provider -- when you reach whatever site through a VPN or by using a proxy server, you share the limited bandwidth that VPN or proxy has with other users, so your connection often slows, sometimes quite a bit.
Another advantage is that you can use their DNS server[s] by setting their IP address as the DNS server your router uses. That way any device using that router -- any device using your network -- takes advantage of that service. The disadvantage of setting SmartDNS as the default DNS server is that while it's not hard really, it is more hassle to switch your DNS server to use SmartDNS, or not, than it is to for example toggle the switch turning the Opera browser's VPN service on/off.
A VPN in contrast generally provides a special encrypted connection between you and one of the VPN's servers, so that no one has access to anything passing through that connection, e.g. your ISP or government can't capture &/or monitor anything. Using a VPN when you type in giveawayoftheday[.]com in the address bar of your browser & press Enter, you connect 1st with the VPN's server, and it in turn sends a request to a DNS server to connect with that site, then passes the contents of that site back to you over that encrypted connection. Since that request came from the VPN's server rather than from you directly, the GOTD site will see the VPN's server IP address rather than your IP address. While that part is the same as using SmartDNS, you have the advantage that everything reaching your network is encrypted, with the disadvantage that you may have reduced bandwidth depending on the VPN service's resources.
keepsolid[.]com/smartdns/manuals/setup-smartdns-on-windows-10-8-7-vista-xp
wikipedia[.]org/wiki/Domain_Name_System