Alça vs. asa
While both alça and asa can translate to "handle" in English, the choice depends heavily on the shape of the object and the regional variety of Portuguese. Generally, alça implies a curved strap or loop, while asa implies a wing-like projection. In Brazil, alça is the generic term for almost all handles, whereas European Portuguese makes a distinct separation between the two.
Alça
B1This word refers to a strap, a loop, or an arched handle. In Brazil, alça is the universal word used for handles on cups, mugs, buckets, bags, and backpacks. In Portugal, its usage is more specific: it usually refers to flexible straps (like on a backpack or a top) or a handle that arches over the top of an object (like a bucket handle).
A alça do balde de plástico arrebentou.
(The plastic bucket handle snapped.)
Ele segurou a xícara pela alça com cuidado.
(He held the cup by the handle carefully.)
Preciso costurar a alça da minha mochila.
(I need to sew the strap of my backpack.)
Esta mala de viagem tem uma alça resistente.
(This suitcase has a sturdy handle.)
Asa
A2Literally meaning "wing," this word describes a rigid handle that projects from the side of an object. In Portugal, asa is the standard term for the handle of a mug, teacup, or the side handles of a pot or traditional basket. In Brazil, this usage is extremely rare; calling a mug handle an asa sounds odd to Brazilians, who almost exclusively use alça instead.
A asa da caneca partiu-se quando caiu no chão.
(The mug handle broke when it fell on the floor.)
O cesto de vime tem duas asas laterais.
(The wicker basket has two handles on the sides.)
Agarra a panela pesada pelas duas asas.
(Grab the heavy pot by the two handles.)
Não consigo segurar a chávena porque a asa é muito pequena.
(I cannot hold the teacup because the handle is too small.)
Summary
To summarize, if you are in Brazil, it is safe to use alça for almost any type of handle, from bags to coffee mugs. If you are in Portugal, you must distinguish the shape: use alça for straps and arched bucket handles, but use asa for rigid handles that stick out from the side of mugs, baskets, pots, and vases.