What is the difference between ubuntu-18.04-server and ubuntu-18.04-live-server?

It always helps to read the Release Notes.

https://wiki.ubuntu.com/BionicBeaver/ReleaseNotes

The next generation Subiquity server installer, brings the comfortable live session and speedy install of Ubuntu Desktop to server users at last.

N.B., If you require LVM, RAID, multipath, vlans, bonds, or the ability to re-using existing partitions, you will want to continue to use the alternate installer

From Update to Release notes. But still some issues, see notes for full details.

As of 18.04.1, the Subiquity server installer now supports LVM, RAID, vlans, and bonds.