Are 无期 and 无限期 same? As you know, when you say 无期徒刑, that means it is a lifetime prisonment or the term is limitless until your death, but recently the news said a Chinese singer claimed that he would 无限期 stay out of career due to his wife getting videoed having an affair with a male model, but two or three months later, he resumed his singing career at the jeer of fans, who thought he broke his promise.

Are they the same?
无期 (without time limit) in '无期徒刑' is short for '无限期' . However, the term '无期徒刑' itself is a common set phrase for 'life sentence' . Therefore '无限期徒刑' is considered incorrect phrasing of "life-sentence' , although it is not grammatically incorrect. ('无限期' as an adjectival phrase that modifies the noun '徒刑')


无限期 (without time limit) is a phrase made up of 无 (without) and 限期 (time limit). 


When used as an adjective, it requires an adjective marker '的' as in '无限期的徒刑' (jail sentence that without a time limit)
When used as an adverb, it requires an adverb marker '地' - as in '无限期地監禁' (indefinitely imprison)
'无限期' can also be an adverbial phrase, and modifies a verb without marker, as in '无限期罢工'


无期 (never) in '會再无期'(no date/ never to meet again) is an adverb