It's not really medieaval but rather Renaissance (though these are both fluid terms) and the Landknechts belong to the bridging period between what is roughly speaking considered medieval armies and early-modern (often distinguished as when units become more permanent features rather than made up from whoever showed up to the muster).

The thing you are most likely talking about are the Doppelsöldner, literally double-wagers. These were the elite or experienced troopers of a Landsknecht formation making up abtou100 out of each unit of 400. These more dependable troops would often be issued halberds or indeed zweihänder (ie two handed swords) and were used for bodyguard detachments (for officers and the standards) and holding the front and rearmost ranks (ie the ones most exposed). The Doppelsöldner would also supply a unit's arquebusiers. So becoming an arquebusier was one way to advance from being "just a pikeman".

The Doppesöldner would be given more prestigious duties, ones that required experience (like guarding important targets) or more skills and were paid accordingly. So I would suggest that is indeed what you are remembering. As they would be armed with weapons more useful in a more open type battle with early firearms and poleweapons which would allow them to be effective in smaller units.

That said I don't think the idea of double pay is strictly speaking only applicable to these experienced/elite Landsknechts, but they do sound a lot like what you are asking about.

Doppelsöldner and Landsknecht would in this case be the terms to look up. I've been using "MAA 058 The Landsknecht" by Douglas Miller, 1996 reprint to quickly answer this.