What is the difference between an applicator tampon and a non-applicator tampon?

Simply: applicator tampons have an applicator, non-applicator tampons don't.

Applicators were originally included with tampons because the Catholic church was concerned about women touching their own genitals, they continue to be popular in the US because of attitudes Americans have towards female anatomy. Non-applicator are a better option as they're simpler, more hands-on, and give better control so they're easier to insert - also it means less waste.

With the average woman using around 12,000-16,000 tampons in her lifetime, adding that amount of plastic to landfill too represents a significant environmental impact.