Smooth is a very common term and has a lot of meanings; my question is on smooth meaning:
Ingratiatingly polite and agreeable.
Is smooth commonly used with that meaning and is it a synonym of 'polite' or has it different shades of meaning?
This is a common usage. Consider this definition from OD
(Of a person or their manner, actions, or words) suavely charming in a way considered to be unctuous: his voice was infuriatingly smooth
The popular song by Sade, Smooth Operator describes a man who is polished but insincere
A license to love, insurance to hold
Melts all your memories and change into gold
His eyes are like angels but his heart is cold
A similar term is slick
Smooth and superficially impressive but insincere or shallow
It's meaning is based on it's usage.
This is a very smooth surface
He smoothed over my disappointment with kind words.
She adjusted the folds with a smooth of her hand.