do you mean the whole faith as in universal? i was always taught there was the word Catholic with the large C and the word catholic with the small c.
You were taught correctly, for practical purposes. Your question, however, also gets into the theology of what the Church is.
On a purely day to day level, Catholic, as in Roman Catholic or Eastern Catholic, is a proper name. So it is capitalized, like other proper names; New York, Mary, or whatever.
The word catholic means universal, which is how much (not all) of Christianity understands itself - Christianity is meant to be the religion of all people. In this sense, almost all churches consider themselves catholic. Some churches use the word in this way only - some share the sentiment but do not use the word catholic.
Many of the churches who tend to deliberately use the work catholic, however, tend to mean a bit more than that - they see themselves very much as part of, or constituting the whole of, the Church which has existed since the beginning, instituted by Christ. Many recognize apostolic succession in some form. Catholics, under the Pope clearly fall into this, seeing themselves, and the Orthodox, as constituting the whole of the Church. The Orthodox, though they tend to use the word orthodox, also recognize themselves as catholic - they believe they alone constitute the entirety of the Church. As well, Lutherans and Anglicans fall into this group - the reformers in those churches did not see themselves as breaking away or starting a new church, but rather reforming the catholic Church. Historically their view on Catholics and the Orthodox has varied somewhat. There are some others in this group too.
So as you can see, Catholics consider themselves to be catholic, and exclude Protestants from this, but many Protestants also claim to be catholic and believe in a catholic Church… The Orthodox, on the other hand, say they are all just Protestants
Clear as mud?