Hi woollymammoth,
The type of account is usually indicated on the mail server settings website from your email provider.
As you mentioned, the menus are different for iPhone to select the same options. Make sure you've configured according to your email provider and the manual setup steps show here:
Enter account settings manually
If Mail can't find your email settings, then you need to enter them manually. Tap Next, then follow these steps:
1. Choose IMAP or POP for your new account. If you aren’t sure which one to choose, contact your email provider.
2. Enter the information for Incoming Mail Server and Outgoing Mail Server. Then tap Next. If you don't have this information, try to look it up.
3. If your email settings are correct, tap Save to finish. If the email settings are incorrect, you'll be asked to edit them.
If you still can't set up your email account or save your email settings, contact your email provider.
Add an email account to your iPhone, iPad, or iPod touch
While not comprehensive, there is a lookup tool that might find your account settings, but your mail provider will also have them listed on their support site:
Mail - Official Apple Support
Thanks for using the Apple Support Communities.