School of Buddhist thought. Typically refers to lineage.
For example, the main "division" of Buddhist thought is to the Mahayana and Theravada branches (or, depending on whom you ask, Theravada, Mahayana, and Vajrayana.)
The Mahayana branch consists of two main schools, Zen and Pure Land (there were others, but these are the two main ones nowadays).
The Zen school contains two major sects, or lineages, namely Soto and Rinzai. These are so named after two famous Chinese monks (though, Soto and Rinzai are their names as pronounced in Japanese).
There is nothing sectarian about Buddhist sects! They are not opposing schools of thought, nor is there any animosity among them. They simply developed whenever a prominent monk came up with an original method of passing dharma on others.
A good analogy explaining that Buddhist sects are not competing would be a Harvard physicist and a Yale physicist. Both were probably trained in physics somewhat differently, but they both are physicists first and foremost. Similarly, a Soto Zen Buddhist is a Buddhist first of all, a Zen Buddhist second of all, and a Soto Zen Buddhist third of all. Whether one is a Zen Buddhist, or a Theravadin, or a Tibetan Buddhist, one is simply a Buddhist and views all other Buddhists as such.
The Buddha himself encouraged the creation of various sects because dharma transcends culture. It is not necessary for a Chinese Buddhist to embrace Indian culture. Nor does an American have to cast away American culture and become a Korean (fill in any other traditional Buddhist culture) to be a Buddhist.
Indeed native American schools of Buddhism are likely to develop over a period of time (as are European, which will probably have many diverse sects since there are many distinct cultures in Europe).