Not exactly. There are many kinds of crosses. By way of example:Don't think so. Don't have time to look up this am to confirm.
Catholic cross isn't straight lines. Ends of the arms & upright are enlarged and elaborate in design. Compare theirs to the cross on the "Christian" flag for an example.
- Celtic cross has a circle in the center.
- St.Andrew's cross is shaped like an X.
- Greek cross has the upright and the the cross piece the same length.
The cross most often worn by Catholics isn't a cross at all, but is called a crucifix. The difference is that it contains an image of Jesus hanging on the cross. Catholics do not wear rosary beads as jewelry.
I agree with the proposition of the OP that too little thought is given to the significance of the cross by those who wear them. However, I would rather see it displayed often than not see it displayed at all. It speaks to the fact that we are a Christian culture, albeit rather weakly.