I haven't tried loads of them just yet, but it's my understanding if it says the purpose shows only "Desktop", it would be only the
live version, and probably not include a built-in means of installing to HDD. And if it mentions "OS Installation", it
is set up to install to hard disk. But, even the live-only ones likely can be installed with some third-party helper software, and/or manually by the technically inclined. For instance, many Linux versions are supported by
LinuxLive USB Creator for installing them to any USB drive.
IIRC the ones showing "rescue" are specifically designed for repairing failed/unbootable Windows. In my experience, some of these live Linux distros may not be full Linux distros (likely ones showing only the rescue function) but mainly tailored to the rescue purpose.