Norimaki & Makizushi both refer to the rolled up sushi. Makizushi is used more commonly used than Norimaki. INterestingly Google has 2.28M occurrences of Norimaki but 4.85M of Makizushi.
Makimono (lit: rolled up thing) covers rolled sushi but also describes calligraphic scrolls.
From my experience, older people to use the term Makimono, whereas makizushi is very heard. I've never had a conversation where the term "norimaki" came up, and I used to work in a Japanese restaurant with people form Nagoya, so maybe that one is regional.
Searching the usual Japanese resources did not yield any definitive answers.
PS: Inuit have over one hundred words for snow (ref: http://www.mendosa.com/snow.html). So if Korea only has one word, I guess that shows how important a part of Japanese culinary culture sushi is :D Of course Korea rules when it comes to Bulgogi/Yakiniku.
EDIT: Fixed for anthropological accuracy, and to garner an up vote from @Hippietrail