[quote=ICXCNIKA]It is my understanding that so called Christians who deny the Trinity, Oneness Pentecostals for example, are not considered Christians since they deny the nature of God.
Oneness Pentecostals are primarily considered to be non-Christians because they do not have a valid baptism: They baptize in the name of Jesus only, rather than in the name of the Trinity (“Father, Son, and Holy Spirit”). Ontologically speaking, they are not Christians because they do not have a valid baptism. Theologically speaking, they deny the Trinity and thus do not hold to classical Christian orthodoxy.
[quote=ICXCNIKA]If that is true, why is it that we consider Christians those who deny the Real Presence of Jesus Christ in the Eucharist? What is the difference?
Most non-Catholic Christians who deny the Real Presence of Christ in the Eucharist (e.g., Baptists, Seventh-Day Adventists) have valid baptisms. They are ontologically Christian. If they believe in the divinity of Christ and in the Trinity as well, then they are also theologically Christian.
It is a valid baptism that makes a person Christian. If a person is baptized validly with the proper matter (water), the proper formula (“In the name of the Father, and of the Son, and of the Holy Spirit”), and with the proper intention (to baptize), that person is ontologically Christian (i.e., Christian is something that person is). If the person believes in the divinity of Christ and in the Trinity, then that person is theologically Christian (i.e., he has Christian beliefs). However, as baptism imparts a permanent supernatural character upon the soul, a person’s status as a Christian is not dependent on how well he either understands or practices his faith.