If you ask different instructors what a given technique is called, or precisely how to do it, then you will usually receive lots of different answers.
Some people might call a simple outward swinging motion an outward swing or a swing outward, while others might call it an external rotation or an outward shoulder rotation, or whatever other term they prefer to distinguish it from other techniques. If you look for different instructional videos or articles you might come across a variety of different terminology to describe the same sort of actions.
Similarly, for the same simple outward swinging motion, you may observe that 10 different instructors will teach it 10 different ways. Which way is correct? Well, they can all be correct for achieving different goals – depending on the precise details of how you perform an action, it will work this or that muscle, or it will work the same muscle but in different ways, or it may resemble this punching technique or that cutting technique with a sword.
There is no “one true way” to perform any given exercise, but there are definitely lots of ways to perform exercises badly. Anything that puts unnecessary strain or stress on your body is probably bad, and anything that twists your body or limbs in unhealthy ways is probably bad. Anything that leads to you injuring yourself is definitely bad! So while there is no “one true way” to do things correctly, you still need to make sure that you are not doing things wrong, to avoid injuring yourself.
If you observe different instructors teaching the same technique in different ways, you will probably notice that certain elements of the technique remain the same, even if the overall shape is a bit different. It is worth paying attention to this if you are watching lots of different videos of people using Indian clubs.