Different kernel versions across different machines

Solution 1:

Ubuntu 18.04 either upgraded from a prior release (17.10 or 16.04 LTS) or installed with the original ISO, or 18.04.1 ISO uses the standard kernel 4.15.

Ubuntu 18.04.2 and later ISO installs default to using the HWE or hardware-enablement stack kernel, ie. the kernel upgrades to using 18.10's kernel, then 19.04 (5.0 is the current 19.04 kernel being used), then 19.10 kernel, before finally settling on the 20.04 kernel.

The HWE kernel can also be selected as an option for older 18.04/18.04.1/upgraded-to-18.04 machines too.

One of your machines uses HWE kernel, one does not.

Installing the HWE stack is simple:

DESKTOP

sudo apt-get install --install-recommends linux-generic-hwe-18.04 xserver-xorg-hwe-18.04

SERVER

sudo apt-get install --install-recommends linux-generic-hwe-18.04

https://wiki.ubuntu.com/Kernel/LTSEnablementStack