RUDOLF:
Absolutely. The formation of primitive gut is one of the first stages of development. After some initial cell replication from the zygote, we begin as a hollow ball of cells. An area that will eventually become our anus on that ball folds inward (invaginates) and stretches all the way across to the other side creating a new opening. This new opening is the primitive mouth. Think about that next time you're kissing someone.
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Both the interior of the mouth and the anal canal are made of non-keratinized stratified squamous epithelium. The outter lips and its lower doppelgänger are made of thin keratinized squamous epithelium.
If it makes you feel any better, despite the similarly, the lips are actually not a sphincter, butt four independent muscles.