Sensitiviy and Resolution in Windowing Functions
I object to the Wiki author's use of the words "resolution" and "sensitivity." Those words are vague and the author does not define or explain them in any meaningful way. If I was forced to use the author's poor terminology I'd say, "A fine-resolution window is a window having a narrow main lobe. (And windows whose main lobe widths are narrow have high-level sidelobes.) A window with good sensitivity is a window with low-level sidelobes. (And windows with low-level sidelobes have wider main lobes.)

I do not understand the 2nd and 3rd paragraphs of your question.

A window with a narrow main lobe improves your ability to distinguish (recognize, discriminate), in the frequency domain, two closely spaced spectral sinusoids.  A window with low sidelobe levels improves your ability to detect, in the frequency domain, a low-level sine wave that is close in frequency to a high-level sinusoid.