Idolatry is, as the name suggests, that which concerns the worship of idols.
Since they (idols) are not God, idolatry is the worship of whatever is not God. That is, anything that is not God; a creature of God.
The difference is in the fact that an idol is anything which is worshiped despite its not being God. This means that if it is not worshiped, then it is not an idol.
That is, the difference between a statue or a gold figure or whatever else, and an idol, is its use or non-use as such.
Therefore, statues (such as those God Himself commanded be made: Ex 25:18; 37:7; 1 Kgs 6:23, 32; Num 29:9-10) are not always idols period.
Thus, since Catholics do not, and are not, allowed to worship statues, but only venerate them as to the prototype (person) they represent (just as one kisses a photo of their love one, by which they mean to show love to their loved one, not paper or ink) there is no idolatry.
In fact, idolatry being a mortal sin, if one dies unrepentent of idolatry, that is, having worshiped anything or anyone who is not God, they will go to Hell.
"These relics are usually the remains or possessions of a great saint. Many of these relics are believed to give divine blessings of various types, including healing for the sick. This seems to fit the definition given of an idol."
This cannot be so, since we see this approved of in Scripture; and obviously, as the context shows, by God (who worked these miracles):
Acts 19:11-12 (DRB)
And God wrought no ordinary miracles by the hands of Paul, so that even there were brought from his body to the sick, handkerchiefs and aprons, and the diseases departed from them, and the wicked spirits went out of them.
Why don't healing relics count as idols?
Simply because idolatry involves worship; accepting healing through any instrument of God, on the other hand, is not.
Clearly, we can't disrespect a relic or item through which God works miracles or did so. It remains for us, then, to reverence or show respect for these channels of God's miracles and/or grace. Which are by definition, by that fact, holy.
We never worship a relic, or even the saint (Acts 10:25-26; 14:5), just venerate or reverence them (just as we don't worship a king, even though we do, and should, reverence them as the authority or representative of God in some way—whether through miracles or anything else—among us—Jn 19:11; Rom 13:1). There is a great divide between the two: and it resides in the heart and nowhere else.
How could God's own work through His instruments of various kinds possibility diminish His glory or detract therefrom? Isn't it the converse? Isn't that why, precisely, that He does these things (to make His power known through his saints in whom He is happy to show His generosity and power)?