¿Son todos sinónimos? En nuestra lengua parece que sí.

Borrasca, tormenta, tempestad, temporal, tromba, tifón, torbellino, huracán, tronada, inclemencia, cellisca, vendaval, aguacero, ciclón.

Y en inglés tienen mas palabros. 

blizzard
a storm with a lot of snow and strong winds

cyclone
a severe storm in which the wind spins in a circle

duster
a dust storm

dust storm
a storm during which a very strong wind blows a lot of dry soil around

electric storm
a storm with thunder and lightning (=loud noises and bright flashes of light)

hurricane
a violent storm with extremely strong winds and heavy rain

rainstorm
a storm with a lot of rain

snowstorm
a storm with a lot of snow and strong winds

southwester
a strong wind or storm that is moving in a south-west direction

squall
a storm that happens suddenly, especially at sea

storm
an occasion when a lot of rain falls very quickly, often with very strong winds or thunder and lightning

tempest
a severe storm with strong winds and heavy rain

thunderstorm
a heavy storm with thunder

typhoon
a tropical storm with strong winds that move in circles

windstorm
a period of bad weather when there is a lot of wind but no rain

a gathering storm
a storm that is coming