According to the Bible we are called to honor God (for example, the first three of the Ten Commandments) as well as one another (for example, 1Peter 2:17).
The specific kind of honor we give God is not the same kind of honor we give to humans. This distinction is made in Greek because two different words are utilized (latria for the honor given to God and dulia for the honor given to humans, and there is a category within dulia called hyper-dulia meaning a special kind of honor given to Mary).
Traditionally such a distinction was not made in English. The words “honor” and “worship” were originally interchangeable, and the context told you if it referred to God or humans. As proof of this, consider the fact that in American English a judge is called, “Your honor” while in Britain a judge (i.e., magistrate) is called “Your worship.”
At some point in the early 20th Century there was a desire to give English the kind of distinction that is found in Greek. Therefore, a gradual trend happened in which one saw the term “worship” being used exclusively for God (or other divine persons in the case of other religions). Therefore, when you see Catholic literature or hymnals referring to the “worship” of the saints or Mary, check the publication date and you will inevitably discover that it is about 100 years old or older. In other words, it was published at a time when the words “worship” and “honor” were considered interchangeable.
Such books that continued to be published later in the 20th and 21st Century will probably have been edited to replace the word “worship” with “honor” (when applied to Mary and the saints) to reflect the new trend in the English language to restrict the term “worship” to the concept of the honoring of divinity.