You can find some wonderful resources on the internet for temari making and here are two places to visit where you can find lots of help with terminology.
Barb Suess has consolidated a set of definitions and illustrations onto a single web page here. There are also several links (in red type) that will take you to step by step pages and other additional learning resources.
Temarikai also has a long list of how tos in the toolkit here. There are also definitions on other pages.
Why is it important to use the same words? Well simply it helps us all to communicate effectively. Temari makers are scattered across the globe and we all speak our own native languages (even English is different based on which country you live) so by learning a unified temari language we can all understand each other and discuss temari concepts in spite of our own language differences.