Eloping

Hi, i`m 18 and me and my g/f want to elope, but the problem is we`re not quite sure what eloping actually means. What we think eloping is getting married but only in the eyes of the gov., so then we can just get married and only us knowing about it, then in acouple years, around 21, we want to have a big wedding with out family and all. So we think eloping is just getting married in the eyes of the gov, not the church, and then when we actually want the wedding, we can in acouple years so we can be married in the eyes of the church too. I want to know if the statement i just made is true, and if not, can you please clarify for me, thank you.