A/B testing, offline experiments, machine learning modeling experiments are methods of testing hypothesis. However, there are some key differences between the these methods.
Differences
A/B testing is controlled online experiments. It is conducted online with real users in live environment. It is mostly executed in e-commerce settings.
Offline experiments (or Field Experiments) are also controlled experiments. These are not conducted online, but in field e.g. telephone calls, surveys, pamphlet.
Machine Learning modeling experiments are not controlled. Here are the focus is to build machine learning model by trying different feature engineering and algorithm.
Similarities
All of above use statistical methods to determine wining candidates .
Example
A/B testing: A website owner might run an A/B test to see which headline performs better on their homepage.
Field experiment: A health company give a drug and determine impact
Offline experiment: A company might run an offline experiment to see which sales pitch performs better at a trade show.
Modeling experiment: You try multiple feature engineering approaches, algorithmic approaches to determine whether you can build a model that can do classification/forecasting
Which method to use when?
Here are some considerations
If your hypothesis is about people preference online controlled experiment or a/b test is right approach.
If your hypothesis s about people health/long term behavior changes - you will do offline experiment in controlled manner.
If your hypothesis is about data patterns, you will do modeling experiment to determine whether you can identify pattern and train model.