Helping clear up the confusion....
How far in advance should we book a celebrant/officiant?
Assuming you're going for a non-religious ceremony, it's good to start looking for your officiant after you've confirmed the date and venue. (Um, because without this person the wedding's just a big party!) If you start interviewing officiants 9-12 months before the wedding date, you'll have plenty of time to choose someone who fits your beliefs and style, and to create a ceremony that reflects your vision. Obviously elopements are different, and in that case just call your ideal person to see if they're available.
What's the difference between an officiant, celebrant, minister, or family member/friend who performs the ceremony?
It's gotten a bit confusing, hasn't it. <Sigh.> Ok, here's the low down. There are a number of options available to you to make your marriage legal. I use the term "officiant" to describe anyone legally entitled to perform your wedding. After that the roles diverge, primarily along lines of religion.
A minister is most traditionally someone of a religious faith who serves a congregation or community in person. Ministers usually go through education and training at a seminary or divinity school. These are your rabbis, priests, pastors, UU ministers, etc.
In recent years, organizations have popped up that will administratively "ordain" non-religious, untrained, lay people, usually referred to as online ministers. These are folks with ordinations from AMM, ULC, Church of the Flying Spaghetti Monster, etc. These officiants are recognized by some but not all states. (And confusingly, by some but not all counties/cities/towns in a state. You'll need to do some homework.)
Celebrants are professional officiants. They are usually trained in ceremony design, ritual, interfaith unions, and in handling all the legal and professional aspects of performing the wedding (from public speaking skills to sound systems to state marriage requirements). They must also be legally recognized to perform marriages, and so must either be a minister, online minister, or civil servant.
Fulfilling simply the legal requirements for performing marriage, are civil servants like judges, Justices of the Peace, county clerks, etc. In some cases, civil officiants are bound by law not to incorporate any religious or spiritual elements.
Finally, many states will temporarily deputize anyone who wants to perform a specific wedding on a specific day, usually called temporary officiants. There's some administrative overhead and a small fee, but this is how your family member or close friend is able to legally marry you on the day of.
How do I choose?!
If you're traditionally religious and want rituals in your ceremony that can only be performed by a priest or rabbi, look for a religious minister. This may also narrow your venue choices, so those go hand in hand and should be planned together.
If you want a very personal ceremony, or you're spiritual, interfaith, or 'culturally religious', look for a professional celebrant. Celebrants are trained to develop your cultural traditions, personal beliefs, and wedding day vision into a coherent and moving ceremony. They will also be credentialed and aware of the legal in's-and-out's of making sure your marriage is official. Bonus: they've usually worked with a number of other wedding pros already and become a natural part of your team.
If you're looking for a standardized civil ceremony that gets you legally married, go for a civil servant like a judge, Justice of the Peace, or county clerk.
If you want something personal and inexpensive, but are willing to handle all of the legal paperwork, ceremony creation, and logistics, such as educating yourself on the legality of day-of/online officiants in your municipality of marriage, ensuring the correct documentation, confirming the license was signed and submitted properly, validating the officiant's status, sound systems, etc.—then ask a family member or friend to get designated.
Phew - hope that helped!