Culverine, saker & falconet are all names not used in the German artillery systems, while "Falkonet" and "Falconet" the same gun with the name spelled a bit diffrently
To complicate matters even further there several parallel artillery systems in Germany/HRE with even the Habsburgs not havning standardized their artillery. And to add insult to injury the Germans insisted on multiple weird spellings for their own artillery designations.
The Culverin is roughly equal to the German "Schlange" in that both were gun types distinguished by very long barrels. The Germans would then further classify a "schlange" as a full, 3/4, 1/2 or 1/4 "Schlange" with additional types being the "feldschlange" and the "notschlange". A 1/2-Schlange could be anything from a 12 to an 18 pounder.
The "Saker" was a very unusual gun type in Germany and typicaly imported from England. Known as a "Sagro" according to Furttenbachs period manual.
The Scharffentinnle aka Scharffendindl aka scharffendink and so on was a very light cannon which typicaly fired a shot of 1/2 or 3/4 pound. Barrels were 7-8 foot long in the pieces I can find data for. (
The Falkaune/Falckaune/Falkohne was the medium field piece with a typical caliber of 4 to 6 pounds. (7 & 8 pounders of this type existed as well but the lighter versions were more common.)
The Falkonet/falconeth/falkhenet was the light artillery piece with a caliber of 1 to 3 pounds, the 3-pounder was often called a "double" Falkonet.
Scharffentinnle & the lightest of the falkonets would commonly be used either from a wall or other fortification and could also be mounted on a wagon for use as part of a wagenburg. I don't think I have ever seen evidence for their use a fieldpiece.
Falkaune & the heavier falkonets were used as field artillery on the field of battle as well as part of a fortress or towns artillery. As most 16th C artillery they were pretty much static once deployed.
Culverines or more properly "Schlange" came in a wide variety of sizes, the smaller ones were used as field artillery while the heavier ones were primarily for siege use. (But would be used in battle as well if there was time and the right ground.) As a rule the Schlange always weighed more than other cannon of the same caliber due to their long barrels. For example a 6-pound Falkaune had a barrel lenght of about 10-11 feet while a 6-pound "Schlange" had a barrel of 15-18 feet. Danish 16th cannon of the "Notschlange" type had barrels that weight 4300 to 5300 kilos(!)(As a comparison the 24-pounders recovered from HMS Wasa had a weight of about 1300 kilos.)