Although there is no word in Buddhism for either of these things, the idea of promoting the Dhamma as widely as possible began with the Buddha himself and was important in Buddhism for many centuries.
After the Buddha accepted his first disciples, he said to them: ‘Go forth for the good of the many, for the happiness of the many, out of compassion for the world, for the welfare, the good and the happiness of gods and humans.
Let no two of you go in the same direction.
Teach the Dhamma which is beautiful in the beginning, beautiful in the middle and beautiful in the end. Explain both the letter and the spirit of the holy life, completely fulfilled and perfectly pure.’ (Vin.I,20).
Unlike some missionaries of the main monotheistic religions, Buddhist missionaries never collaborated with invading armies or colonial occupiers to spread the Dhamma. There are also almost no examples where force or legal sanctions were used to promote Buddhism.
The last great Buddhist missionary endeavour to meet with widespread success was the conversion of the peoples of the southern Himalayas (Kinnaur and Sikkim) during the 16th and 17th centuries by monks from Tibet.
The Buddhist revival in Sri Lanka in the late 19th and in Burma in the early 20th century started in part as a reaction against the arrogance and aggression of some Christian missionaries. See Conversion