That title may sound a bit strange, and, you bet, it was a typographical error for an interfaith meeting. Usually the word "faith" in "interfaith" is associated with a major religion, and not with a particular sect of a religion. Hence in an interfaith meeting you will see representatives of Islam, Christianity, Buddhism etc., rather than a representative of Shia, Presbytarian, Theravada etc. So in the context of usage of the word "faith" in "interfaith," an intrafaith meeting would comprise representatives of sects within a religion: say, a meeting of Buddhists from Mahayana, Tibetan, Theravada etc. traditions.
You rarely hear about any such intrafaith meetings being held. In some religions, the differences between sects had led in the past and continues to lead even now to bloodshed. In some other religions, although there may not be a violent interaction between the sects, there is enough disharmony that the sects rarely see each other eye-to-eye. So why is it easier to profess brotherly feelings for followers of other religions but not with those from one's own?
I can think of two reasons. Let us look at them, considering Hinduism as an example, noting that the same holds for any other religion too.
1. The underlying fundamentals of all the sects in Hinduism are the same (Vedas) with differences only in practices or interpretation of scriptures, while catering to the same mass of people (largely of Indian origin). Since the same foundation (Vedas) is being interpreted by each sect differently, there is, in some counterintuitive way as a conflict of interest, more of a sense of disunity amongst the sects than they would have if they were having an entirely different fundamental basis. Also, each sect clamors for greater acceptance amongst the masses to have more followers, and this "cut-throat" competition completely contravenes the idea of brotherhood amongst the sects. However, these very sects in Hinduism will easily accept a sect of any other religion, say Christianity, that originated in an alien land, as there are clear demarcating fundamental differences (Vedas and Bible), and also they are prevalent amongst a different geographical/cultural populace.
2. Many people within a religious sect sincerely believe that their own path is the best - if one is ruthlessly sincere, this opinion will be found within oneself. Some people openly admit this view and profess the same to others, whereas others, due to propriety, may withhold it within oneself. So striking a conciliatory note with other sects would be seen as an act of acknowledging other paths as equally valid if not as good as one's own. This attitude of superiority of one's own path is also carried to interfaith meetings, where one begins to feel that one's own religion is superior to others (since now there are no sects to contend with). When it is said that one's own ideal is the best, it is meant as "the best for oneself," but not "the best of all ideals." The mental make-up of a person resonates with one particular path (sect), and hence it is best suited for that person whereas it could be not so helpful to some other person.
In the old days, the divisions in Hinduism were based on whether one was a follower of Vishnu, Shiva, Durga, etc. (considering only the aspect of Personal God in Hinduism). Many of us may ridicule the prevalent sectarian divisions of those times, forgetting that we ourselves are afflicted with a similar disease nowadays based on whether one is a follower of Ramana Maharshi, Sai Baba, Ramakrishna, Chinmayananda, Sankaracharya etc. Very often the followers of these teachers disagree with the methods prescribed by other teachers, and rarely do they meet with each other to resolve or to understand such differences. Amazingly, the universalism of Hinduism that professes "the whole world is a family" (vasudhaiva kutumbakam) is usually forgotten by these very sects of Hinduism when amongst each other, but the same is emphatically proclaimed in interfaith meetings when amongst different religions.
We should ask ourselves sincerely, "Have I really made efforts to reach out to sects within my own religion with whom it is more difficult to reconcile? Do I, deep in my heart, feel that my ideal is superior to others, and if so, what efforts am I doing to negate this false sense of superiority?" I think a person will do much better with a little more introspection on this front, along with indulging in an intrafaith dialogue before merely attending an interfaith meeting and turning it into a pompous show. Jesus Christ said, "Leave your offering there before the altar and go, first be reconciled with your brother, and then come, bring your offering" (Matthew 5:24). By "brother," He meant not only the neighbor (interfaith) but also the one within one's family (intrafaith).