Hi!

I'm a bit confused about the 2 "Mode" options for any selection tool:

example images:

https://drive.google.com/file/d/1xsUXwAjwBDSKcKs3cYanL7RyWho2AZlm/view?usp=sharing
https://drive.google.com/file/d/16NT7RwkOr1g4Lc7ZoQ97ZJuuQf37Mv86/view?usp=sharing

What exactly is the difference between them, and the practical use of the different modes ?

The "Pixel Selection" mode lets you turn off anti-aliasing, but if you can also turn it on in this mode, what is the use of the "Vector Selection" mode , then?

Initially, when reading at the Krita User Guide, I had the impression that using the "Vector Selection" mode allowed me to have an editable selection path, like a vector path but for selection mode. ( without needing to create a regular vector path/shape and them turning it into a selection area)

Can someone explain it to me?

"Initially, when reading at the Krita User Guide, I had the impression that using the "Vector Selection" mode allowed me to have an editable selection path, like a vector path but for selection mode. "

Yes, it does and a good way to understand it is to use it. You could try the following exercise if you have a bit of time:

Paint a broad wavy line across your canvas on a paint layer to give you something to look at and work with.

Use the polygonal selection tool to make a vector selection in the form of a jagged shape like a star, or whatever. The dotted outline that you see is a representation of the outline of a shape that has been drawn on the Global Selection Mask (GSM). All selections are some kind of image on the GSM. Actually, you can also have Local Selection Masks (LSMs) which are local to a single layer but we'll stick with just the GSM.

That shape has been drawn as a vector polygon, i.e. not raster painted, and as such it can be manipulated with the vector editing tools. To do that, you need to operate on the GSM:

Do Select -> Show Global Selction Mask and the GSM selection layer will appear at the top of the Layers docker as the selected layer and so the GSM itself will appear on the canvas as translucent red = not selected and transparent = selected.

Use the Select Shapes tool to click/select the shape on the GSM, then a standard shape editing box will appear around it and you can manipulate the handles on this to move/stretch/rotate it, as a vector shape.
Choose the Edit Shapes tool and the vertices of the vector polygon will appear as control points and you can then use all the vector shape manipulation techniques on it to drag vertices around, add control points, put curvature on line sections, etc.

Now click on the paint layer in the layers docker and you're back to seeing a dotted line selection that you've manipulated with the vector editing tools.

Like everything else, it gets more complicated as you get deeper into it but that exercise should illustrate the basic principle.