Linux Shared Hosting
Windows Shared Hosting
With VPS Hosting, you will have administrative access to your VPS. Hence, you are allowed to send both SMTP authenticated and non-authenticated emails. Be sure you don't keep your VPS as the open relay and don't send spam emails. It may cause your VPS IP address to get blacklisted in spam databases like SpamCop, SORBS, Spamhaus, URIBL etc.
Note: It is recommended to clean your email list before starting an email campaign to reduce bounceback. check out the best email validation service.