So even they are confused
The word "cyclone" has a couple of different meanings. The first meaning is as depicted in unworry's picture above.
But the term "cyclone" in meteorology also means any closed, rotating low-pressure system. So both Hurricanes and Typhoons are types of cyclones. Tornados and even dust devils are also type of cyclones.
And yes, somewhat confusingly, a Cyclone is also a type of cyclone.
Since
cyclone means a closed
low-pressure system, an
anti-cyclone is any closed
high-pressure system.
It's good for pilots to be familiar with this second definition of cyclone because sometimes we will see the term depicted in meteorology charts, reports, etc. E.g., a cyclone might be forming over Colorado, or an anti-cyclone might persist over Germany.
More:
some definitions of Typhoons, Hurricanes and Cyclones.