There were dozens of different types of swords in widespread use in central Europe during the 16th century, with various different types used on one hand or in two, and each had common regional names and morphological distinctions that make it difficult to have an agreed-upon modern nomenclature.
Andre Paurnfeindt, a fencer, author, and trabant or bodyguard to Matthaue Lang von Wellenberg, wrote a fencing treatise in 1516 that covered the use of the sword in two hands, sword in one hand, staff, dagger, and sword and buckler. The latter two were reprints of a much earlier work by Andre Liegnitzer.
Paurnfeindt introduces the sword in two hands thus:
This chapter teaches how one should gain advantage with the long sword, which is used with both hands; much like the battle sword, riding sword, estoc, and many others that I will leave out here.
The second chapter, on the sword in one hand:
The Second Chapter teaches how one must wield the messer with advantage, which has become increasingly useful due to its manifold uses. The tessack or messer is a predecessor and source of the other weapons that are used in one hand, such as the tessack or tucke, the katzbalger or the hand degen, and others I will leave out for the sake of brevity.
These two brief intros give us nine swords:
longsword
battle sword or schlachtschwert
riding sword
estoc
messer
tessack
tucke - another verson of estoc, as above
katzbalger (here as Spatel or spade)
hand degen - Degen being a common word that just meant sword, and had a few common variants, such as the Raufdegen and here the Handtegen
Each of these would have a great many variants, and Paurnfeindt's Austrian dialect would likely have used local regional terms for swords known by other names elsewise. There's also confusion in using similar terms for two very different types of sword, for instance the Triecker given in the two handed chapter I've rendered as estoc, which was a term used for a type of sword in two hands used for fencing in armor that often had a rigid blade and reinforced point, and included a place about halfway up the blade for a fencer to grip, and in the one handed chapter there is Tucke, which could mean a dagger, such as possibly a Swiss dagger or Hauswehr, a type of quite short point-oriented sword favored by the Swiss, or could have been a different word for rapier, as both Sydney Anlgo and Ewart Oakeshott give a definition of Tucke/estoc as a thrust-oriented sword in one hand, which might be understood today as an early form of the rapier.
But by including Liegnitzer's sword and buckler section, we also introduce a sword commonly called an arming sword, which had quite a few variants as well.
Following all this up, in Ewart Oakeshott's arms research, he classifies an early form of german complex hilt swords in one hand as "Landsknecht hilts", commonly called katzbalger nowadays, and a later elaboration being "German saber hilts" that were precursors to the "Sinclair saber" hilt commonly used in the 17th century. These were likely both used for weapons called in the Fechtbucher genre the dusack or tessack, coming from the Hungarian for "tusk" or "fang," and involved a complex hilt on top of a saber blade, likely imported or inspired by curved blades used in Poland, Hungary, Bohemia, and the Ottoman empire.
Fechtbuch writers that followed Paunrfeindt, such as Joachim Meyer, also included the rappir, rappier, or rapier - all just variant spellings - in their teachings, and we can see long, slim-bladed swords meant for one handed use with complex hilts in public proliferated woodcut art and in private art as early as the 1520s. Diving into artistic rendering and swords as social tags is a whole other layer to all this
Without writing an entire book I can tell you that there were dozens of different types of commonly carried swords in the 16th century, and central European citizens, mercenaries, and men-at-arms had access to just about every form you could desire.
For more I'd recommend Ewart Oakeshott's European Weapons and Armour: From the Renaissance to the Industrial Revolution as a start
To add a couple more to u/partymoses's answer that aren't specifically German. The "cortelacio", "curtilace", "curtal-axe", or early cutlass was popular in the 16th century among men-at-arms, who would carry it at the saddle in addition to their arming sword and mace.
Second PartyMoses already covered the estoc, but on horseback you also had the polish "Koncerz" originating in eastern europe which was likewise called a "Tuck", "Tock" or "Estoc" further west. The Koncerz was a long, stiff, one-handed or two-handed thrusting sword used either a bit like a one-handed lance for after the lance had already broken or used to stab at soldiers down on the ground while still high up on horseback. This sort of sword started also being used by some horsemen further west as Sir John Smythe recalls in 1594: "Howbeit I haue seene some both men at armes, and dimilaunces vse tocks very conueniently worne after the Hongarian & Turkie manner vnder their thighs; which Tocks are long narrow stiffe swords onlie for the thrust."
This sword would also usually be worn at the saddle with another sword, such as an arming sword, cutlass or saber.
Sometimes though "Tuck"/"Tock"/"Estoc" could refer to a much shorter thrusting sword though, so it's a bit of a messy term.
