I have a Spanish sword with a blade not too dissimilar to those. Could be a generic style? I would struggle to classify the German sword above as a rapier. Also the blades were typically made in a fairly small number of centres and sold all over to cutlers who fitted hilts to the blades according to their customers’ preferences. There were guilds which separated the trades of the bladesmiths and the cutlers.
I found this site which is interesting.