These two points are still circling around the same meaning. Having a strategy means you know how to use a specific trading approach, which makes it called a "strategy." If A trades with an indicator in a way, and B trades with the same indicator, but with a twist, that means B has created a strategy different from A, despite using the same indicator. But still, they are their strategies, not anything else.

Perhaps you wanted to explain it from the angle of a "trading system." If that is the case, then you need to explain a different term entirely, other than calling it a strategy.