What Is The Application Launcher?

I had OpenSuse installed for about 4 hours until I gave up on the wifi card.
Strangely, Kubuntu was able to configure it properly out of the box.

However, I don’t like the look of the application launcher as much.
I prefer a launcher that folds out the sub-menus width ways rather than sliding on top of each other.

What is the name of the application launcher in OpenSuse?

assuming you’re talking about plasma 5, there are 3 launchers to chose from, you could have right clicked on the start button and selected alternatives to see the other 2 alternatives, they are not developed by opensuse but by the kde teem,
about your wireless card some firmware is not open sourced and are not included in the obs repositories or in the Linux kernel but you can find drivers for them on packman or you could have asked in the wireless forum
https://forums.opensuse.org/forumdisplay.php/676-Wireless
kubuntu is a fork of a fork of a fork, comparing it to opensuse is pointless

Lets leave the driver discussion to the wireless thread when I get around to it.

Maybe it is just the theme that is confusing me.

Is opensuse using Lancelot by default with Plasma 5?

No.
Lancelot is dead, at least it hasn’t been ported to Plasma5.

The default one openSUSE uses is called “Kicker”, and is based on the KDE4 “Homerun” that was available as extra package. It exists in a full screen version too (“Kicker Dashboard”), and Kickoff is still available as well (and actually still the upstream KDE default).