Picture the hours a person normally gives to work or study in one week as a single container. Full-time can be thought of as that container being filled right up, with nothing left over. Everything the word does comes from that picture: the job that fills it, the student whose week is filled, and the joke about a puppy that fills it without paying you.
Wiktionary gives the origin simply as full + time, which matches the modern picture: a time that is full.
來源把這個字的組成寫成 full 加 time，也就是「滿的時間」。這跟今天的用法對得上：時數被填滿。
Wiktionary (kaikki snapshot 3f6f69a190036ae4), full-time, adj: From full + time.
Two branches
工時或課時被填滿
這是字面上的用法：容器裝滿的就是真正的工作或就學時數。
adjective · B1
Filling all the hours of the week that people normally work or study, not just some of them. It can describe a job, a course or a person, and it can also describe how someone works: she works full-time.
全職的；全時的
誇張說法：把你一天塞滿的事
同樣是「時間被填滿」的畫面，只是拿來形容根本不是工作的事，效果就變成誇張。
adjective · B2
If you say that something is a full-time job, you mean it takes so much time and effort that it fills your whole day, even though it is not really a job you are paid for.
（忙得）像一份全職工作
以下是外部詞典記錄的用法，原文照列，我們還沒有寫成教學內容。上面的說明才是我們自己寫的；有些用法可能上面已經講過了。
full-timeadj/ˌfʊl ˈtaɪm/
Involving a full amount of time spent on some activity, especially a job.
full-timeadv/ˌfʊl ˈtaɪm/
Spending a full amount of time.
資料來源：英文維基詞典 English Wiktionary（CC BY-SA 4.0）。 原文照列，未經改寫。