The term first got attention when the Obama administration started using it, seemingly in lieu of "freedom of religion," after the Fort Hood shooting in late 2009. People complained, there was a bit of noise, and then the furor died down.
But it leapt back to the minds of many conservatives during the "Catholic contraception" flap.
"Freedom of worship" is different from the traditional term because of the popular definition of "worship." In general usage, worship is what you do at "church" (whether the religion is Christian, Jewish, Muslim, or something else entirely). Freedom of worship, then, would seem to mean your right to do "church" your way — be it liturgical or casual, with incense or without pianos.
Reading about the contraception rule, I saw many articles or comments with this idea: "What's the problem? We're not telling them they have to hand pills out in church?" That is the essence of the freedom of worship.
Freedom of religion, on the other hand, extends beyond what happens on Sunday. It's tithing and evangelism and caring for orphans. It's also pacifism, infant baptism, and opposing abortion (for, respectively, Quakers; Roman Catholics and some protestants; and a great many Christians, Jews, and Muslims).
If we only have a right to "freedom of worship," there is nothing to stop the government from conscripting Quakers or forcing evangelical churches to perform same-sex marriages. (I'm not saying either of those things is on the horizon, but there's nothing to stop it.)
But there is something. Read the entire text of the First Amendment:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.The first freedom enumerated was the freedom of religion, and "free exercise" is explicitly stated. This nation was settled by people who were fleeing pressed military service or laws about baptism just as much as those who wanted the right to wear certain robes (or not) in church.
It's natural that non- and cultural-Christians should be opposed to our ideals. The world opposes us reflexively because of Christ. And our attempts to live up to a higher standard makes people feel bad about their lower standards. And the wisdom of this age is that personal liberty and a right to "privacy" (that is, doing whatever you want in private) trumps all other rights.
However, this being expected doesn't mean we should just sit back and watch it happen. We can and should watch our politicians like hawks and push back where we can.
Remember the words of the Master: "I am sending you out like sheep among wolves. Therefore be as shrewd as snakes and as innocent as doves."