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?
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.