刚 (gāng) and 刚才 (gāngcái) both translate as "just", but they work differently. 刚 is an adverb that goes before the verb. 刚才 is a time word meaning "just now" or "a moment ago".
Subject + 刚 + verb.
刚 goes after the subject and directly before the verb. It means something happened only a short time ago, and "short" can be a few minutes or a few months, as the speaker feels it. You don't need 了 at the end: 我刚到 is a complete sentence.
刚才 is a time word, like 今天 or 昨天. It can go at the start of the sentence or after the subject, and it only means a few minutes ago.
Because 刚才 is a time word, it can do things 刚 can't. Only 刚才 can start a sentence: 刚我吃了饭 is wrong. Only 刚才 can come before a noun: 刚才的电话, not 刚的电话. Only 刚才 can go before a negative: 刚才我没有听见, never 刚没有.
刚 can do things 刚才 can't. It can go with a length of time (刚来两个月), and with 就 to say that one thing happened right after another: 我刚到家，就下雨了.
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