Thought I needed to create a subset listing of vim commands for vi, but the nvi implementation (and probably the original vi) has basic commands that work the same way as vim. The main observed difference is really (credits to SO):

• Backspace only deletes characters during the current insert mode session, and not after the characters have been committed during previous inserts.
• The line display not updating on backspace delete, so it looks like the cursor is moving backwards without deletion.

vi-specific behaviours can be enabled on vim using :set compatible. For vi deletion, use the usual d or x commands, or use X for backspace-like behaviour.