What do the words Catholic and Protestant mean? Also, what is the history of use and what languages do they come from? Is it a fitting name today or is it outdated? How do the two relate to each other?
Catholic can have a few different meanings. It could refer to:


The Roman Catholic Church
Eastern Catholic churches in communion with the Pope 
The universal church


The Nicene creed which is used in a lot of Christian churches that have broken away from the Roman Catholic church still say that they "believe in one holy and catholic". (note the lower case letter 'c' in catholic.) Catholic in this context does not refer to the Roman Catholic church, but to a holy Universal church.

Protestant refers to churches and/or individuals who call themselves Christians, but disagree with the Roman Catholic Church.


  The word 'Protestant' derives from the protests made by German princes
  at the Second Diet of Speyer in 1529. The Diet voted to end the
  toleration of those who followed the teachings of Martin Luther within
  Germany (source)


They generally follow the teachings of leaders of the reformation (e.g. Luther). They are called Protestant because they protested the teachings of the Roman Catholic church. The original Protestant movement came from within the Roman Catholic church. The teachings of the protestant movement disagree with Roman Catholicism and a number of the reformers were put to death because they taught these things.

Do these terms still fit today? I don't think this can be answered objectively, but I feel that they are still a correct fit. Mainstream Protestant denominations still hold to the Five Soli. From my understanding, these beliefs do not fit with the Roman Catholic church teachings and so Protestants are still protesting the Catholic Church