Or, less awkwardly, Lutherans are Protestants. The Lutheran church started in Germany. Other churches started in other countries, such as the Anglican church in England. Several other Protestant denominations split off from the Anglican church.
They didn't; Protestant is the generic or umbrella term, for all those
who followed Luther & others, who objected to Catholic teaching.
Lutherans are just one denomination, among many Protestants.
Lutherans are Protestants.
Not all non-Catholic Xians are,though.
Eastern, Coptic etc, Prue date the Roman church.
Also, groups like Quakers and Baptists are not technically Protestants, they are Dissenters. Protestants took over formerly Catholic churches and started new traditions as a protest against Rome, Dissenters gathered somewhere and started from scratch.
Lutherans split off from Catholics, at least according to the tale. Other protestants also often split from Catholicism, such as the Church of England which was encouraged by some British king. Others like Methodism are "revivals" of Protestant faiths, or simply a permutation of the faith in a different culture.