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Mormons are more quick to use the word worship, RC's cleverly avoid that word.
The verb to worship, like the verb to pray, has undergone considerable development. The EWTN website has an informative article on the meaning of worship:

Saint Worship?
Not long ago a diocesan priest was celebrating a wedding Mass. The bride had been raised a Catholic, but the groom had not. He was a recent convert. His entire family and almost all of his friends at the wedding were non-Catholics.Since most of the bride's guests weren't Catholic either, it turned out that few people at the Mass understood what was going on, so the priest added explanations at appropriate points.
It's traditional, at the conclusion of a Catholic wedding ceremony, for the bride to take a bouquet of flowers to a side altar and lay it at the feet of a statue of the Virgin Mary, at the same time praying to Mary, asking for her intercession (cf. 1 Tim. 2:1-4, Rev. 5:8, 8:3-4), that she might be as good a wife and mother as Mary had been.
A bad choice of words
When the time came for that gesture at this particular wedding, the priest tried to explain. He said that the placing of the flowers is done because "we Catholics worship Mary." There was a collective sigh from the few Catholics in the church and a collective gasp from the non-Catholics, who felt their worst suspicions confirmed.
Was the priest right or wrong? Well, both. He was right, given his understanding of the word "worship," though he was using it an almost archaic sense. He was surely wrong in using it in front of people who would misunderstand his meaning.
In common speech "worship" means the adoration given to God alone. In this sense Catholics don't worship Mary or any of the other saints. In fact, the Catholic Church forbids any adoration to be given to any one or any thing but God. But in an older use of the term "worship" could cover not just the adoration of God but also the honor given to anyone deserving of honor.
Begin with the word itself. It comes from the Old English weorthscipe, which means the condition of being worthy of honor, respect, or dignity. To worship in the older, larger sense is to ascribe honor, worth, or excellence to someone, whether a sage, a magistrate, or God.
But there are different kinds of worship, just as there are different kinds of honor. The highest honor, and thus the highest worship, is given to God alone, while the honor or worship given to living men or to saints in heaven is of a different sort. Idolatry thus does not simply mean giving worship (in the old sense) to living men or to saints; it means giving them the kind reserved for God.
Nowadays, there is a problem using the word "worship" because in the popular mind it refers to the worship of God alone. For practical purposes it has come to mean nothing else than adoration. Although it was commonly used in the wider sense as recently as the nineteenth century (when, for instance, Orestes Brownson, an American Catholic writer, produced a book called The Worship of Mary), it is usually too confusing to use it that way now, as the example of the priest shows. It is wise to restrict its use to God and to use for saints and others terms like honor and veneration.
Is this distinction without a difference? It would be if the worship given to God were the same as the honor given to a saint. But it isn't.
The term "worship" was used in the same way in the Bible that it used to be used in English. It could cover both the adoration given to God alone and the honor that is to be shown to certain human beings. In Hebrew, the term for worship is shakah. Its appropriately used for humans in a large number of passages.
For example, in Genesis 37:7-9 Joseph relates two dreams which God gave him concerning how his family would honor him in coming years. Translated literally the passage states: "'[B]ehold, we were binding sheaves in the field, and lo, my sheaf arose and stood upright; and behold, your sheaves gathered round it, and worshipped [shakah] my sheaf.' . . . Then he dreamed another dream, and told it to his brothers, and said, 'Behold, I have dreamed another dream; and behold, the sun, the moon, and eleven stars were worshipping [shakah] me.'"
In Genesis 49:8, Jacob pronounced a prophetic blessing on his sons, and concerning Judah he stated: "Judah, your brothers shall praise you; your hand shall be on the neck of your enemies; your father's sons shall worship [shakah] you." And in Exodus 18:7, Moses honored his father-in-law, Jethro: "Moses went out to meet his father-in-law, and worshipped [shakah] him and kissed him; and they asked each other of their welfare, and went into the tent."
Yet none of these passages were discussing the worship of adoration--the kind of worship given to God.