There are two conjugations for Spanish imperfect subjunctive: -ra and -se. Many teachers ignore that and teach them as if they were the same or just straight up instruct learners to use -ra exclusively as it is the most common form across all the Spanish-speaking world.

Although this approach is okay, there is nothing wrong in learning more and being able to use both forms properly, which is why I decided to write this article.

After reading this article, you should be able to properly use both forms.

Why are there two forms?

There reason is, as you might guess, history. Latin used to have a past perfect form, from which the -ra forms come, while the past subjunctive made it to Spanish as -se.

§24.2a El pretérito imperfecto (cantara o cantase) es el tiempo más complejo del modo subjuntivo, tanto por los contextos sintácticos en los que se usa como por la variedad de los significados que expresa. La variante en -ra del imperfecto procede del pluscuamperfecto de indicativo latino (amavĕram ‘había amado’), mientras que la variante en -se procede del pluscuamperfecto de subjuntivo (amavissem ‘hubiera amado’). Esta última forma sustituyó a su vez a amārem, que era originalmente pretérito imperfecto de subjuntivo. La sustitución de amārem por amavissem empezó por darse en contextos modales, en especial condicionales, lo que anticipaba el importante cambio gramatical que cantara experimentó en la historia del español, al que se aludirá en los § 24.2h y ss. ¹

They can be used interchangeably most of the time.

When is it wrong to use them interchangeably?

• In conditional sentences. Read more in this post. The short version is that you can use either in the si-clause (prótasis), and only -ra/-ría in apódosis. It is allowed to use -se in the latter in case of a compound tense (hubiese cantado etc.), but -ra is still preferred over it.
• Only -ra in standalone sentences with the archaic past perfect interpretation. (This tense cantara can be then interpreted as either canté or había cantado depending on the context.)
• Only -ra in “quién-sentences” ² (¡Quién fuera él! [≈‘I wish I were him’ etc.]).
• Only -ra in “imperatives” (“Te hubieras callado” [≈‘You should have shut up’ etc.]).
• Only -ra in “I would like;I/You should” and such sentences that substitute conditional (quisiera, debiera, and such, replacing querría, debería etc.).