The reason I stopped to think about which word to use in the first place was because “internet” sounds more official/professional than “online” to me. The type of website I’ll be creating will be something non-industry related that might benefit from the more “official sounding” name.
For example, I would rather be an account holder at xxhttp://www.InternetBank.com rather than xxhttp://www.Onlinebank.com.
What a weird little topic.