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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?

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JPEG2000 is not always lossless. You can use it lossless, but mostly, it's used to compress images in a lossy way. – slhck Feb 4 at 22:10
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BMP is both uncompressed and lossless. PNG is compressed but lossless. Thus, with a lossless format the only visible difference is the file size. I'd recommend using PNG over BMP unless you can't for compatibility reasons.

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You said visible difference. Should there really be any difference except for file size? – user1032421 Feb 4 at 22:13
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That is correct. The pixels will be 1:1. – iglvzx Feb 4 at 22:15
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PNG also supports transparency while BMP doesn't. – dnbrv Feb 5 at 4:05
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