Converting to Apple lossless

I have a slightly complicated question regarding lossless music and ITunes. When I buy music on ITunes, it downloads in m4a at 256Kbps. There is an option, however, if I go to 'File' then 'Convert' to turn a song into Apple lossless. Then a copy of the song appears in my library. Upon right clicking, selecting 'Song Info', then selecting 'File' in the pop-up window, I can see that the Kbps is considerably increased from the previous version of the song I had. It seems to have worked as the file size has gone up and it does appear to be downloading something for a second before appearing in my library, but I also have my reservations. So my question is; did ITunes download a higher sample rate song, or is it the same quality, just sampled more?