There is a difference.

Année is used to express a notion of duration which is not in "an" (unit of time):

J’ai travaillé cinq ans dans cette entreprise (simply informative)

J’ai travaillé cinq années dans cette entreprise (we want to underline the fact that it is a long time)

They are not really interchangeable — since in some situations one is nearly always used and the other isn’t — but using one instead of the other will often be understandable, just non-idiomatic or losing a nuance.

As a rule of thumb,

• an is used for the unit of time;

• année is used for a period of one year, usually contiguous, often with a implied precise beginning (1^st of January — année civile —, 1^st of September — année scolaire —, date of birth, …).

• using année tend to focuses on what happened during the time span while using an focuses on the duration. For instance

  • deux ans de travail de perdus emphasises the lost time (which could have been used for something else)

  • deux années de travail de perdues emphasises the lost work (perhaps it has to be redone)

I see another difference we may add to other answers.
When we talk about a period of time in the History, we use the term années :

Cette technologie a été inventée dans les années 2000.

I’m not sure that soirée/matinée/année have to be about specific or special occasions or durations but they have some properties setting them aside from soir/matin/an:

1. they do not have to be contiguous:
   • +J’ai passé deux années en Malaisie, 1991 et 2005
   • ?J’ai passé deux ans en Malaisie, 1991 et 2005
2. they are compatible with internal quantification:
   • +toute la soirée/matinée/année vs ?tout le soir/matin/an
   • +la soirée/matinée/année entière vs ?le soir/matin/an entier
   • +pendant la soirée/matinée/année vs ?pendant le soir/matin/an

3. In general, ans seems to avoid indefinite plural contexts:

   • ?des ans, ?quelques ans vs +des années, quelques années

And so it happens that we get :

• un million d’années and not ?un million d’ans

As French has this strange thing with 1 000 000 which must be constructed as an NP taking the counted noun as an indefinite complement the same way un grand nombre does:

• un grand nombre de chats
• un million de chats

This naturally excludes ans from this context while allowing it in:

• un million trois cent mille ans & un million trois cent mille années