I attended a Catholic school
Me too. I love how the Catholic Church created a parochial schools for the masses 
Are they same as missionary schools?
I am not sure but it seems so since the church supported 43,800 secondary schools, and 95,200 primary schools. That was in 2016
OK is it government funded?
No it was not government funded but their deeds led to development of numerous native religious congregations which established schools, hospitals, orphanages, reformatories, and workhouses.
They helped sharpened education around the world
Oh yes you get it even tough they encountered various struggles following the creation of the Church of England
Interesting, I would like to know the rivalry between both parties?
It was because Anti-Catholicism in this period encouraged Catholics to create modern Catholic education systems to preserve their tradition