Which of these terms you prefer may simply be a comfort level with one or the other, or a preference for how one word sounds. I am perfectly happy being described with either term.
Some people prefer "Officiant" because they view my role as official -- perhaps in the sense that I may be conducting a ceremony that has legal recognition, or that I (momentarily) am an official of the state. "Celebrant," which some think has a New Age-y or spiritual sound, is what others prefer. It would also be correct to refer to me using the term "Minister," which is what I am and what my title is at the Unitarian Universalist Fellowship in Clinton, Iowa where I currently work (and though I am technically neither, I also have certainly been addressed as "Pastor" and as "Sister"). Somehow, "Mother" never seems to serve as the feminine appellation alongside "Father," and I simple cannot guess why...
Whatever you call us, there are several questions you should be sure to ask before booking anyone to officiate or celebrate your marriage ceremony.
Are you available for my wedding date and time?
Will you have other weddings that day?
(If so) How much time will there be between ceremonies?
What are your religious requirements, if any?
Are there specific religious words or terms that you insist on?
(If pertinent) Do you object to the race/gender of my fiance?
Can we choose our own vows and readings?
Can we include ethnic or cultural traditions?
Will you attend (and conduct) a rehearsal?
What will you wear during the ceremony?
What is your fee? Are there any other charges?
Do you require a deposit?
Will you provide an advance copy of exactly what you will say?
Answers to these can help you determine whether a particuar officiant is right for you. In any case, a clergyperson should be willing to meet with the two of you in person and discuss these issues before you actually book them for your wedding date (i.e. before you pay any deposits or fees, and before you sign a contract or letter of agreement).
I, like any other minister with experience conducting wedding ceremonies, can easily answer all of these questions in full. Those answers should easily help determine whether an officiant is a good choice for you.