The surname Chanler, like Chander, occurs quite frequently in the censuses of English-speaking countries, usually as a mis-hearing of Chandler. The issue of variant and deviant surnames is a significant problem to genealogists. The further back in time records were written, the greater the likelihood of variants and deviants being encountered.
A variant is a change from the original surname which is continued through many generations and becomes a name in its own right. Chandler was itself probably a variant of Chaundler which occurred hundreds of years ago.
A deviant, on the other hand, is a temporary corruption of the original surname, which is corrected later in the same generation or quickly thereafter, with subsequent offspring reverting to the original "correct" surname. Deviation can be caused by many factors, or combinations of factors - an accent unfamiliar to the (often ageing) person making the record; bad pronunciation; poor hearing; delay in making the record, combined with forgetfulness, etc. And the reason the errors often went unnoticed was that the person whose name was being recorded was illiterate, so unaware of the error and unable to correct it.
So, although a Chanler record is usually a short-lived deviant of the name Chandler, in the case of this genetic family 31 it has been sustained to the present day, and is therefore a variant.