I COULD HAVE AND I SHOULD HAVE

Hola amigos I recently came across a Spanish sentence that said "Podria haber ido al cine anoche," which I understood to mean "I could have gone to the movies last night." This was in a text book, so I assume it is correct. However, I seem to recall that another way to say this sentence would be "Habria podido ir al cine anoche." Is this second version right? Do they both mean the same thing? Maybe the translation varies from country to country. Or maybe it's my poor old brain getting tangled up on me! I have the same question for those occasions when I want to say that I should have done something. Is it "Deberia haber ido al cine" or "Habria debido ir al cine"? (Sorry for all the missing accents.) Thanks in advance for any help you can offer me.

Hola Tango! All of the sentences above make total sense!!! and yes, they are different versions of it!... the last one could also be put as "Debi haber ido al cine", but the ones you suggest are correct! So, stay calm, your "old brain" is working just fine!! i would say, above average ;) saludos desde Mexico!

Hola Cristian Thanks for your reply to my recent question. I always appreciate receiving your expert comments and advice. Feliz Navidad and best wishes to you and your family for the coming holiday season.

Hola! Feliz navidad y prospero año nuevo!!!

Hola Chicos!! Interesting ... which would be correct in conversation then?