Painting with pixels means to apply blobs or clusters of colored pixels to the raster while thinking like a painter would think with traditional brushes and paint.
The difference in (strict) Pixel Art is that the newly placed pixels do not blend or mix in any way with the pixels which are already there on the raster but instead fully replace them (unlike paint which mixes with the paint already on the canvas).
Most Pixel Art editing software still has a multitude of painting or brush modes and layer effects though which can still cause a placed blob of pixels to blend and mix with the pixels that are already there.
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