These are two names for the same behaviour — keeping a partner hidden from your friends, family and public life. 'Stashing' emphasises where you're put away; 'pocketing' emphasises being carried but concealed.
Side by side
Aspect
Pocketing
Stashing
Behaviour
Hiding a partner
Hiding a partner
Image
Kept in a pocket
Stashed out of sight
Public presence
None
None
Difference
Interchangeable terms
Interchangeable terms
What each one means
Pocketing
Pocketing is when someone you're dating deliberately keeps you hidden from their friends, family and social media — no introductions, no public acknowledgement — as though the relationship is being kept tucked away in a pocket.
Stashing is dating someone while deliberately keeping them hidden from your friends, family and social media — so the relationship never becomes publicly real.