I'm Catholic and ex-Protestant, but have no difficulty with the Catholic teaching on receiving communions viz. only those who truly believe the bread and wine represent the flesh and blood of Christ. There's a link here which explains the reasons.
For the same reason, Catholics are not supposed to take communion outside the Catholic Church, although we probably could in (some or all?) Eastern Orthodox Churches, as they hold the same view of communion as we do.
Why can't non-Catholics, Evangelicals and Protestant denominations receive Catholic Communion?
My wife is Baptist, so she belongs to a church where communion is merely symbolic. Yet whenever I go to a Protestant service, there seems to be something missing, and as far as I'm concerned it is the symbolic communion. The music might be better, the sermons might be better, but something is definitely missing.
As for the technical difference in terminology between Mass, Eucharist, and Communion, I've given a brief explanation below along with some links and extracts.
1. THE MASS
link -
http://www.stjohnslincoln.com/files/timb/timb-02.pdf
In a nutshell, the term "mass" is simply a distortion or abbreviated from of "ite missa est", the original Latin expression for the dismissal at the end of the "mass".
2. DIFFERENCE BETWEEN EUCHARIST AND COMMUNION
In practical terms, there's not much. However one sister, an expert in Liturgy said a lot of Catholics wouldn't know the difference, and the two terms are used interchangeably a lot of the time.
However my understanding is that the "Eucharist" is the whole process beginning when the priest begins by blessing and breaking the bread and wine, up to and including our partaking of communion, which is the actual consumption of the flesh and blood of Christ.
The sister commented the Eucharist was a "five stage" process as follows (lifted from a Coptic site this time) -
Sacraments of the Eucharist
5. (My addition) We then eat the bread and drink the wine, hence partaking of the flesh and blood of Christ.
Stage 5 is technically the Communion, whereas the whole process of the priest blessing the bread and wine, "breaking the bread" (which in Catholic Churches is represented by the priest breaking a large waver in half to begin with) and then distributing them, is the Eucharist, for what it is worth.
I don't see any reference by Christ saying the process was purely symbolic, as He used the term "Is my flesh" and "Is my blood". Indeed one requirement that caused many to fall away was his demand that they "eat his flesh" and "drink his blood". To the Jews this was anathema. They would have instinctively understood He wasn't talking in a purely symbolic sense.
He meant it literally.