@Earth Wind and Fire
I think the confusion here arises from the fact that for the most part modern services are fairly non-exclusive. Anyone can come and go as they please, and it's considered extremely rude to ask anyone to leave unless they are causing some disruption.
Traditionally, both in the early days and up until very recently pretty much anyone (even the heretics) could show up at first and hear the Word, but there would come a point in the proceedings where the preaching and teaching of the Word was over. Then all who were not "of the Faithful" would be asked to leave/escorted out, the doors would be closed, and the Eucharist (aka communion) would then be celebrated.
There is a part in the Divine Liturgy as it is currently constituted that reflects this, where after the homily and certain prayers for the Catechumen and others, the Deacon intones, "Let the catechumen depart! Depart! Let none of the catechumen remain! As many as are of the Faithful, again and again in peace let us pray to the Lord...."
Then a couple of litanies for the Faithful, and some hymns, are sung. Then the head Deacon makes a "final check" instruction to the doorkeepers*: "The doors! The doors!" (Meaning, "guard the doors and don't let anyone else in.") Then, once he's sure everything is in order, he intones, "In wisdom let us attend," and the Mystery continues with those remaining confessing their One Faith by the Creed.
(* "doorkeeper" was and technically still is (although it's become less formal) an actual Order of ministry, albeit a minor one.)
"Of the Faithful" was defined as those who had been Baptized and not excommunicated.
Here is a link with more information:
Dismissal of the Catechumens: more on Part V of the series…
So there is a winnowing process as the service moves forward. All are invited to hear the Word preached, but when it comes to communion, it's exclusive not on "saved or unsaved" but on "baptized and keeping the Faith" or not, as judged by the whole Church including (especially) one's own conscience, particularly in the context of the particular relationship with your spiritual father/confessor/elder, who is responsible to the largest extent for your growth in Christ.
Note that these are objective measures, outwardly known (or at least potentially so -- for nothing is hid that won't be revealed, and a man's conscience knows regardless). Unlike "saved or unsaved" which won't ultimately be known until the final judgment.