To answer this question we need to decompose each word so we can find where is the part that relates these words.
The three words have a greek root, as we can see:
Prokaryote: Pro= before, Karyon= nucleus
Eukaryote: Eu= New, after, Karyon= nucleus
Karyotype= Karion, Typos=Type
So prokaryotes are cells without nuclei and evolutive speaking are older than eukaryotes. Eukaryotes on the other hand possess a nucleus and are more recent than prokaryotes. A karyotype is the count and pairing of chromosomes of a eukaryotic organism.
In conclusion: all three words are related to the presence/absence of the nucleus and are related to their evolutive history.