"School" has been use equally as "sect", but to be more accurate, I like the term sect, as there is really sectarian distinction in various schools / monastic institutes. In order words, a school or schools belong to a particular sect, but a school can hold the lineage of several sects.
The sect that does not have authentic lineage is considered as "heretics" and / or "outsider". Thus the term "sect" is neutral as to good or bad, and "authentic" or "heretic".
No lineage then no buddhism. Authentic lineage is very important, there are different type of authentic lineage, they are of scriptural, oral, and mind.