Åland has its own parliament, its own executive government and is generally autonomous from Finland. The cultural heritage though is mostly Swedish.
Speaking Swedish and being a part of Finland, the people of Åland regard themselves as a separate and autonomous part of Finland, and appreciate if you refer to them as one. Do not refer to Ålanders as "Finns", as this can be regarded as rude.
The islands are monolingually Swedish, a point of some contention in otherwise bilingual or, in practice, frequently Finnish monolingual Finland: Närpes, Korsnäs and Larsmo are the only mainland municipalities to be monolingually Swedish.
The relationship with mainland Finland is somewhat complicated, the language and culture being the greatest hurdles. Many Ålanders refer to themselves as simply just that; Ålanders or "Ålänningar". There's also a growing movement towards full independence, although general consensus is for a more independent autonomy from Finland.
Although Finnish is optionally taught in schools, most Ålanders choose not to study it, and while some commercial signs not any official signs though are written in Finnish in addition to Swedish and often English during the tourist summer season, you should not attempt to get along in it. Communication between Finns unable to speak Swedish and Ålanders is done in English, which is very widely spoken, even by many elderly, so stick to it if you can't speak Swedish or something closely related to it. The relationship to all things finnish, whether spoken or written, is complicated to say the least.