I have installed two Ubuntu partitions and they appear to be using two different swap partitions. Is this a safety thing or is it a waste of space? If the latter, how do I set up one Ubuntu to use the other's swap partition?
It's a waste of space - when installing the second Ubuntu you could've just pointed it to the existing swap partition. Actually, I even think the installer automatically configures an existing swap partition to be used if it can find one.
To fix the situation (well, if you consider it a problem), you need to open /etc/fstab file of one of the ubuntus, locate the line which mentions "swap" and change the device name (or partition UUID) there.
The line would look something like
so you can change it to
or, even better, find the UUID of the swap partition and use it instead: