Both of these nouns refer to deceptions—not necessarily falsehoods, but rather, misleading impressions, especially concerning reasons and intentions.
A pretext is a false reason, stated or implied:
She said that she was going home because she was sick, but he knew that was only a pretext; really she just didn’t like him.
Russia claimed that its troop movements were a training exercise; but that was a pretext.
We often use the phrases a flimsy pretext, or a thin pretext—as pretexts are usually easy to see through.
A pretense is a false claim about oneself, a false appearance, or misleading behavior, act:
His claims to fame were just a pretense; he was not well known.
She made a pretense of feeling sorry for his troubles, but really, she was glad.
In fact, pretense can also be used to describe acting and appearances in films and drama, in which case it does not have negative connotations.