The First Amendment to the U.S. constitution has two distinct clauses relating to religion, and they both protect different rights. First, it says "Congress shall make no law respecting an establishment of religion" - this means that the federal government cannot set an official religion of the United States (which is what it means to "establish" a religion). This was meant to prevent the government being unduly influenced by the religious beliefs of one particular faith, and to prevent it from becoming entangled in religion, which the founders believed to be essentially a private matter. This clause has been interpreted by thevery broadly - it means that the government can't even do anything that favors one religion over any other.
The second clause says "or prevent the free exercise thereof" - this means that, in addition to not establishing an official state religion, the government cannot prevent individuals from practicing their chosen religion, whatever it may be. However, there are some limits on this protection. For example, if your religion requires you to take illegal drugs, or to sacrifice animals in violation of local laws, those laws can still be enforced against you, as long as they were meant to be applied generally, and were not passed with the express purpose of preventing religious practices (for example, laws against drug use apply to everyone, not just people who want to take drugs for their religious rites, so they do not run afoul of religious freedom).
Together, these 2 clauses protect what is broadly known as "freedom of religion" and "separation of church and state"
Freedom of religion means, you can believe whatever religion you want and not even government can control your beliefs.
Freedom of worship is the freedom of an individual or community, no matter where they are(in a public or private place), to practice, worship, and observe their religion. It includes the teaching of religion, but does no mean that you must allow someone to teach you there religion. It is generally recognized to also include the freedom to change religion or not to follow any religion.
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