The older way is where you convert the path to a selection and fill that. You end up with filled pixels on a layer. The disadvantage is that it’s no longer a vector path, so if you need to change the filled area, you have to go back and edit the path, convert it to a selection again, and fill it again.
The newer way is fewer steps, faster, and much more flexible: Before you draw, you make sure the Pen or shape tool is set to Shape in the options bar, so when you draw, it creates a shape layer (a layer with vector objects, like Adobe Illustrator). You can control the fill and outline of shape layers directly, using the Fill and Stroke settings in the options bar. And when you edit a shape layer’s path directly (if it is selected in the Paths panel), the fill and stroke update along with the edited path because they are attached to it.
So start by deciding whether you want to end up with a pixel layer or a vector shape layer, and set the options bar to Path or Shape accordingly. Then use the fill method that goes with how you set it up.
And it’s useful to understand that a path alone is not fillable because a path alone cannot be printed or exported; a path is just a framework. If you want a path to create an object that you can fill, print, or export, what you fill with the path must be a pixel layer or shape layer. Only layers can be printed or exported.
Note that when you fill a path as per Ged's instructions, you are putting pixels on the current layer. The path and pixels no longer have any connection to each other and are edited / moved / adjusted independently.