BioStar was a Stack Exchange 1.0 site, back when people could create sites about whatever without the stringent process that exists today. When Stack Exchange 2.0 and Area 51 launched, all Stack Exchange 1.0 sites were given a grace period to decide whether to run through the Area 51 process or to go it alone.
BioStar decided to go it alone, and created their own site. Since they were no longer on the Stack Exchange platform, they lost the biostar.stackexchange.com domain. You can now find them at their new domain, biostars.org.
They were reportedly in contact with Stack Exchange to get a link or a redirect from biostar.stackexchange.com to biostars.org, and that discussion might still be ongoing.