Borsa vs. borsetta
The Italian words 'borsa' and 'borsetta' both refer to types of bags, but they differ in size and usage.
Borsa
'Borsa' generally means a larger bag or handbag. It can also refer to other types of bags or even financial concepts.
Ho comprato una nuova borsa per il lavoro.
(I bought a new work bag.)
La borsa della spesa è piena di generi alimentari.
(The shopping bag is full of groceries.)
La borsa di Milano ha chiuso in rialzo oggi.
(The Milan stock exchange closed higher today.)
Borsetta
'Borsetta' is a diminutive of 'borsa' and typically refers to a small handbag or purse used by women.
Maria ha una borsetta elegante per la serata.
(Maria has an elegant little purse for the evening.)
Ho dimenticato il rossetto nella mia borsetta.
(I forgot my lipstick in my purse.)
La borsetta di designer è molto costosa.
(The designer purse is very expensive.)
Summary
While 'borsa' is a more general term for bags of various sizes and purposes, including large handbags and even the stock market, 'borsetta' specifically refers to a small handbag or purse, typically used by women for carrying personal items.