Complex sentence: The term "public school" is used in the United States to mean what other countries call "state school," a term that sometimes refers to a state university but is almost never used in reference to elementary and high schools.
Split into simpler sentences: The term "public school" is used in the United States to mean what other countries call "state school". "State school" is sometimes used in reference to state universities but is almost never used in reference to elementary and high schools.