What does "to pray" mean in Catholicism? The general usage of to pray in non-Catholic religious settings seems to indicate worship of God, raising one's heart to God, and forms of reaching out or responding to God. However, we often hear that Catholics pray to saints, though Catholicism firmly asserts that it does not condone worship of any being other than God.

Is "praying to Saint So-and-so" a mis-use of the verb to pray? Are worship and/or God not inherent to religious prayer? Or, is are they both correct uses: Are other modes or meanings to the verb intended in certain Catholic uses of it?

It's also notable that Catholics identify several forms of prayer: vocal prayer, meditation, and contemplation. Do those fit within the "general Christian" understanding of prayer?
The Roman Catholic definition of prayer just means to communicate to God or the saints. To "pray" to a deity is to ask the deity for something, which involves communication. This is different from worship, which means to honor or show respect. Because a prayer means communication and worship means respect, prayer may be an act of worship or reverence. When Roman Catholics "pray" to saints or God, they really mean they want to communicate with them, looking at how the saints lived their lives and how that would be an example to present Catholics, which, in my opinion, does not sound too far-fetched from veneration of the ancestors in Chinese folk religion. Whether it is veneration of ancestors or saints, the veneration or worship should not be confused with the adoration of the gods or God. Assuming that the definition of "prayer" means "to ask or to beg a god for assistance", the Catholic definition seems to work nicely.