Anillo vs. sortija

In Spanish, the words 'anillo' and 'sortija' both refer to rings, as in jewelry. These are used interchangeably in some contexts, but there can be certain connotations or uses unique to each word.

Anillo

'Anillo' is a general term for 'ring'. It does not have specific cultural or contextual connotations. It refers to any ring, regardless of its style or the occasion for which it is intended
¿Dónde dejaste el anillo de boda?
(Where did you leave the wedding ring?)
El anillo que me diste es muy hermoso.
(The ring you gave me is very beautiful.)
Voy a comprar un anillo de compromiso.
(I'm going to buy an engagement ring.)

Sortija

'Sortija' is often associated with a more ornate type of ring. While it can also be used to refer to any ring in general, in many contexts it implies a type of jewel-encrusted ring or one that might be given as a gift or sign of affection.
Me regaló una sortija de esmeraldas.
(He gave me an emerald ring.)
Esta sortija fue de mi abuela.
(This ring was my grandmother's.)
Estoy buscando una sortija para el aniversario de mi esposa.
(I'm looking for a ring for my wife's anniversary.)

Summary

'Anillo' and 'sortija' can both mean 'ring', but 'sortija' may imply a more ornate or special kind of ring. 'Anillo' is probably the more common term, while 'sortija' might be used more in discussions of fashion or when talking about a special gift or memento.