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I’ve seen JPEG2000 files with both .J2K and .JP2 extensions, and codecs which read one won’t always read the other. Can someone explain why there are multiple extensions for what I thought was a single format?
Because JPEG 2000 is both a codec and a file format. The standard is in many parts, with Part 1 giving (mostly) codec information (i.e. how to compress and decompress image data), with a container file format annex (JP2). Part 2 gives many extensions, and a more comprehensive container format (JPX).
JP2 is the “container” format for JPEG 2000 codestreams, and is modelled on the Quicktime format. J2K, I’ve not seen (we used J2C during standardisation), but I presume it is raw compressed data, without a wrapper. The point of the containers is that a “good” image comes with additional metadata – colour space information, tagging, etc. The JP2 format base allows many “boxes” of information in one file (including many images, if you like). It also allows the same container format to be used for many other parts of the standard (such as JP3D, and JPIP). Really, you shouldn’t see many unwrapped, raw data streams – it is, in my opinion, bad practice.