Does karma mean fate?

No. Karma literally means "action" or "deed", and the idea is about cause and effect, not about a script written in advance. In the Indian religions, your intentions and actions shape your future: good intent and good deeds lead to good karma and, in traditions that believe in rebirth, happier future lives; bad ones lead the other way. Mistaking karma for fate is so common that the sources point it out explicitly, noting that Sanskrit has its own word for destiny.

The key ingredient is intention. Actions done without intent do not carry the same weight as deliberate ones, and in Buddhism karma is defined as action driven by intention, done through body, speech or mind. In many accounts, nobody hands out the rewards: the law of karma works without any god sitting in judgement, though some Hindu schools do say God distributes its fruits.

The ancient Indians asked the fate question themselves. In the Mahabharata, the prince Yudhishthira asks the elder Bhishma whether a person's life is already destined or can be shaped by effort. Bhishma's answer: both. Your future depends on what you do now, with free will, and on past actions that set the scene.

Karma is not one single doctrine. Hinduism, Buddhism, Jainism and Sikhism all use it differently; in Jainism, karma is even pictured as a fine dust of particles that sticks to the soul. In the West, the idea spread through the Theosophical Society and became "what goes around comes around".