Is that true once someone has cancer that person will always have it, though it's in remission?

Usually: A few cancers can be completely cured by standard therapies, especially "in situ" cancers. However, the best we can do with many cancers is remission - the number of cancer cells in the body are undetectable, but there is the possibility that the cancer might come back. Regular screenings are important in these cases.

The word: 'remission' comes from leukemia therapy. For solid tumors, we use the term 'complete response' when chemo makes something go away, as in testis cancer. If it is removed or obliterated by surgery radiation, the "no evidence of disease" is used. Most recurrences are in two years. Breast and prostate can recur very late, but sometimes not at all.