want = want (desire)
"wanna" is the way English speakers pronounce "want to," as in "Do you wanna (want to) go out for dinner?" Most English speakers do not realize they pronounce "want to" like this until someone points it out to them.
In my EFL classes, I teach my students to pronounce "want to" as "wanna." So, my advise is that you should pronounce "want to" as "wanna," except in formal circumstances: such as in a job interview, or talking to a boss, or delivering a paper at a conference. Even then, native English speakers may use "wanna" in these situations without realizing it.
"Wanna" is not informal. "Wanna" is the normal manner of pronouncing "want to." But sometimes formal circumstances require "want to."