Pretence and pretense are different spellings of the same word. Pretense is preferred in American English, while pretence is the preferred spelling in most other varieties of English, including British and Australian English. Canadian English generally favors pretence over pretense, but the latter appears about a third of the time.
Senior year of high school we once convinced our parents to get us out of school for a day under the pretense that we were sick. [Wall Street Journal]
The president chose to drop any pretense that his administration supports the marriage act. [New York Times]
I met him in a swank and strenuously hip Midtown hotel, a place totally at odds with his lack of pretense. [Sports Illustrated]
Outside the U.S.
The Egyptian government reopened the pyramids to tourists on the pretence that things were getting back to normal. [BBC News]
She will carry on this pretence, she decides, for the rest of the day. [Sydney Morning Herald]
The pretence is that we are in a high school gym watching a competitive spelling bee. [Guardian]