In different programs the same size on “Actual” size shown differently, Bug?

Question

Retina-MBP

I create new files in Pixelmator and Adobe Illustrator. Both files are of 100x100 pixels size. The resolution in Pixelmator is set 300, the resolution of export raster in Illustrator set to 300 as well. I use a retina Mac.

When I press "Actual Size" I expect that both programs will show the same size of the "artboard"/picture.

However, this "actual size" is different within these two programs. Even more - when I export the picture from Pixelmator it has a size of 100x100. However, from Illustrator I get unpredictable sizes of jpegs or pngs.

I completely lost understanding of what happens here. I do not even know what my customers actually see when I sent them the pictures.

When I try the make a screenshot - the pre-mark for PXM is 50x50 and 100x100 for AI! :??