Is SDHC support application specific?

I know the HBC as well as the HBB support SDHC cards as of recently so, once HBC is installed, all applicaitons can be installed from and SDHC card from there on.
However, how about the applications themselves, do they need to support HDHC in order for them to work properly from one such card or since they are running off the HBC the support is implicit?
I'm wondering whether games running off the HBC would be able to save progress and load roms if they don't support HDHC.

Thanks.

SDHC is application specific
Right now all applications on the wii are very monolithic.

There is no shared library that all aplications use to access SD Cards. Every application has to be rebuild with new code

Thanks Daniel.
So it sounds like I should stick to standard SD for the moment to ensure compatiblity, right?