It depends a lot on how it is setup.
You could partition the first disk to allow for multiple filesystems (e.g. /, /boot and others) then partition the second drive to allow for completely separate filesystems (e.g. /multimedia, /mydir, /billybob). In such a setup the space on the two drives is used completely separately so filling one doesn't fill the other.
Alternatively if you were using RAID1 (mirroring) then everything written to the first drive is written to the second drive at the same time so both would reach 100% at the same time.
With LVM or RAID0 mirroring you could make the drives "concatenated" so that the same filesystem uses both drives but fills up one before the other.
There are other raid levels as well though if you only have 2 disks typically you wouldn't be using them.
You might want to provide the output of "fdisk -l", "df -hP" to get more complete answers.