Also known as simple controlled experiment, bucket testing, controlled online experiments or split-run testing. In an experiment like this we have 2 groups and in the simplest version just one variant is different. That`s an user experience research methodology.
In the last years large companies started to use this like LinkedIn, Facebook, Google, Microsoft and Instagram.
Multivariate or multinomial testing is the version where more than 2 versions get tested together in parallel.
Observational, quasi-experimental or other non-experimental situations are unvalid for simple A/B tests.
Two-sample hypothesis tests are appropriate for this.