So what is the difference between the 2?
Firstly, thanks to my colleagues ChrisV and AnujS for the pointers -
The doc glossary states -
Mini campaign - A simplified single stage communication platform that allows a marketer to interact with customers by e-mail or SMS.
Multistage campaign - An integrated multichannel communication platform, that allows a marketer to achieve a specific marketing goal or objective through customer interaction, strategic advertisements and lead generation.
More specifically -
The Mini Campaigns have a single stage whereas Multistage allows one to create multiple stages with different channels to work with, either in sequence or in parallel. Multistage also has the concept of repeatable stages and funneling. When you choose Mini campaign you can only use the email template for email campaigns whereas in multistage, one can create multiple treatments (not just based on a template).
Essentially the mini campaign is built for quick execution, a couple of clicks and you have created one - hence less functionality compared to Multistage.