For starters please compare kernel versions of each. Hardware support is in the kernel not commonly distro-specific.

Slackware 14.2 4.4.14-smp
Ubuntu 18.04 4.15.0-48-generic

"Examining logs, dmesg, kernel log, messages": I don't quite understand.
"... make sure wpa_supplicant and dhcpcd are not started on their own,...": how do I do this?

1. If there is a conflict and two daemons are trying to control the interface it will be somewhere in logs. I do not know what logging daemon you are using, therefore cannot tell you exactly where to look. Possible places are dmesg, /var/log/messages, but there may be more.
2. Your init system has scripts to start daemons, every init system has tools to manage runlevels, again, without knowing details about your system cannot tell what your tools are. For instance, in my OpenRC system I can run 'rc-config' to manage runlevels.

As I previously mentioned hardware support resides in the kernel. My 14.2 Multilib system runs on a custom 5.11.11 kernel which is one of the reasons I prefer Slackware as it works on a vanilla kernel, requiring no special distro-specific hoops to jump through which is common on other distros, especially to support their specific version of package management and auto dependency resolution.

If you aren't familiar with custom building a kernel for yourself (and why would you be coming from a distro locked in to repositories only?) I suggest downloading and installing kernel source and/or headers, kernel package, and kernel-modules and firmware from Current, presently 5.10.27, located in the "k" directory on any mirror, with firmware and a few other important kernel packages in "a". The only minor gotcha one might encounter is if you use the nvidia.foo.run installer which will probably warn you that the kernel was built with a different GCC. Selecting "Ignore gcc check" almost always these days solves that issue.

That version of nvidia installer will succeed and run perfectly even with that minor mismatch AND will almost certainly improve wifi detection, utilization and performance. If you're at all interested in "rolling your own", just ask.

Welcome to Slackware and LQN.

Three possible ways to proceed:
(a) Ubuntu, on the same machine, has no problems with wi-fi. So, comparing the Ubuntu wifi related stuff with that of Slackware a solution could be reached.
(b) To dispense with NetworkManager altogether and use another way of managing the wi-fi.
(c) Try to find a driver for the AC 3160 controller.

I would begin with (b). What other method of dealing with the wi-fi exists besides NM?

Some:

Manual static setup, or manual dynamic. OK if you never travel.
WICD
DHCPCD

And how do I do a manual static setup. I guess it must be fairly complicated.

4.15 kernels have much updated wifi drivers over 4.4 kernels. I would compile my own newer kernel to use with 14.2. Try 4.19 LTS for a start maybe?

Not quite, doesn't Slackware documentation cover it? Init system must be set to bring the interface up and wpa_supplicant conf has to be altered with a text editor.

And why not download the 4.19 LTS, put it in /boot and say lilo to use that kernel? What is the necessity of compiling?

First run "slackpkg update", "slackpkg install-new" and "slackpkg upgrade-all" to check if there are any fixes for 14.2 to be installed. The reboot and check Networkmanager again. If it dies not work; you can try wicd instead:

https://slackware.pkgs.org/14.2/slac..._64-2.txz.html

Restart and click on the wicd icon in your taskbar to add the password for your connection.

As root you can run "netconfig" any time you want to change something.

EXAMPLE - I choose DHCP (second choice) and then use NetworkManager as my means to connect. I have chosen loopback in the past and found that NetworkManager works well with that choice. Try those maybe and see what happens

I don't get it. I choose DHCP. And then how do I use NetworkManager?

I can't run 'slackpkg update' because, of course, I don't have internet in the slackware box.