How do I know which templates will appear in my email when sending emails to a Lead/Contact?

The Record type selected when creating an email template plays the key role to what your contacts/leads will see when receiving your emails.

If you created a template for a project record type this template will not be visible in the public folder when selecting a template to use for a contacts/leads. One of the reasons is that the options available in the drop-down of “Field Type” under “Merge fields” are dependent on the Record Type selected at the beginning of the process.