Boleia vs. carona
The primary difference between boleia and carona is geographical. While both words describe the act of getting a free ride in a vehicle, boleia is the standard term used in European Portuguese (Portugal) and Portuguese-speaking African countries, whereas carona is strictly used in Brazilian Portuguese.
Boleia
A2This word is used in Portugal. To pedir boleia means to ask for a lift or to hitchhike. It can refer to a planned ride with a friend or standing by the road with your thumb up to stop a stranger.
Vou pedir boleia até Lisboa porque não tenho carro.
(I will hitchhike to Lisbon because I do not have a car.)
Podes dar-me boleia para o trabalho amanhã?
(Can you give me a lift to work tomorrow?)
Eles viajaram à boleia por toda a Europa no verão passado.
(They traveled by hitchhiking all over Europe last summer.)
O camionista deu boleia ao rapaz que estava na estrada.
(The truck driver gave a ride to the boy who was on the road.)
Carona
A2This word is used in Brazil. To pegar carona or pedir carona means to catch a ride. It is commonly used for hitchhiking strangers, but very frequently used for getting a lift from colleagues, friends, or family members.
Meu chefe me deu uma carona até o centro da cidade.
(My boss gave me a ride to the city center.)
É perigoso pedir carona na estrada hoje em dia.
(It is dangerous to hitchhike on the road nowadays.)
Vou pegar carona com a minha irmã para a festa.
(I am going to catch a ride with my sister to the party.)
Nós viajamos pedindo carona para caminhoneiros.
(We traveled asking truck drivers for rides.)
Summary
In short, if you are in Portugal, use boleia to ask for a ride. If you are in Brazil, use carona. Both terms effectively mean lift, ride, or hitchhiking depending on the context, but they mark you clearly as speaking either the European or Brazilian variant of the language.