Kılıç is the exact equivalent of the word 'sword' in Turkish. In that sense, it is a generic word. You can call both a 19th century saber and a 15th century scimitar as
kılıçs and gramatically there won't be any mistake in that
Same is true for the word shamsir. In the ottoman context, the only difference is probably while common people called a sword as kılıç, the elite prefered the arabic word shamsir. Within this general category of shamsir/kılıç there are many variations.
There are many experts in ottoman arms here, which i am not, and I think they can better explain the differences in detail.
For the earlier examples of the dress, there are many miniatures and drawings. To give you one example, this is a sketch by Gentile Bellini or by one of his associates. The man in the sketch was probably a member of janissary cavalry (sipahi) of the 15th century.