gewählt
elected
Describes a person or thing that has been chosen for an office or function through a vote or election.
Der neu gewählte Bürgermeister wird nächste Woche sein Amt antreten.
The newly elected mayor will take office next week.

elected / refined
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elected
Describes a person or thing that has been chosen for an office or function through a vote or election.
Der neu gewählte Bürgermeister wird nächste Woche sein Amt antreten.
The newly elected mayor will take office next week.

'Gewählt' is the past participle of the verb 'wählen' (to choose / to vote). It is used as an adjective, and its meanings derive from 'wählen' in the sense of 'aussuchen' (to choose) or 'per Abstimmung bestimmen' (to determine by vote).
Sie hat ihre Worte mit Bedacht gewählt.
She chose her words carefully.
The context makes the meaning clear: If 'gewählt' refers to a person in office (e.g., president, representative), it means 'chosen by election'. If it refers to language, words, or behavior, it means 'cultivated' or 'polished'.
Der gewählte Vertreter sprach mit dem Volk.
The elected representative spoke to the people.
In the meaning 'cultivated', 'gewählt' (refined) is often combined with nouns that describe communication or behavior. Typical phrases are 'gewählte Sprache' (refined language), 'gewählte Worte' (carefully chosen/refined words), or 'gewählte Ausdrucksweise' (refined way of expressing oneself).
Für das offizielle Dokument ist eine gewählte Ausdrucksweise erforderlich.
A refined style of expression is required for the official document.
The meaning 'kultiviert' (cultivated) or 'gepflegt' (polished) belongs to a rather formal and educated style of language. In this context, the word itself already sounds 'gewählt' (refined).
Seine Rede war von einer gewählten Wortwahl geprägt.
His speech was characterized by a refined choice of words.
selected
'gewählt' and 'ausgewählt' both have to do with a choice or with a refined style. The most important difference is: when referring to people or offices, 'gewählt' often means that someone was chosen by a vote. 'ausgewählt' more often means that someone or something was selected from several options. For language and behavior, both can sound very polished. Learners can easily confuse them because both come from 'wählen' (to choose / vote). A practical tip: for votes or elections, 'gewählt' usually fits; for a selection from a group, 'ausgewählt' usually fits.

Nach der Abstimmung war Herr Kaya der gewählte Sprecher des Kurses.
After the vote, Mr. Kaya was the elected spokesperson for the course.
Für die Ausstellung wurden nur ausgewählte Fotos aus dem ganzen Jahr gezeigt.
Only selected photos from the whole year were shown for the exhibition.