I have just learned that PNG is a lossless image format while BMP can be both uncompressed or lossless format. Should there be a quality difference between these two? If not, does it mean that other lossless formats like TIFF, JPEG2000 and PNG offer the same quality as BMP?
There's no quality difference between BMP & PNG format (except PNG is compressed using deflate algorithm).
BMP8 can be compressed using RLE (run-length-encoding) algorithm, but BMP16/24/32/64 doesn't support compression yet.
BMP32 support alpha channel just like PNG32 support transparency.
No difference in quality, both standards are lossless. BMP uncompressed takes more space, but when compressed (e.g. when put in a .zip or .7z file) BMP can be better.
Having done some experiments, I saved a photo in BMP and in PNG, and compressed both files. (.zip) The BMP was 1.8% bigger, but that would vary between photos.
If you are compressing photos, it makes no difference.
However simple picture, such as a drawing you did in paint, or a diagram, will compress much better with .bmp rather than .png.
I again, tested this. I did a logo in paint (similar to a ford logo) and compressed it with 7zip. Uncompressed, the png was 136kb, the bmp 1.7 MB. Compressed, the png was ~100kb and the bmp was 18kb.
If you want to compress pictures, save in .bmp. If not, use .png.
Both when compressed whooped jpeg btw.