Two words or phrases are anagrams when they use exactly the same letters the same number of times, in a different order: listen and silent, dormitory and dirty room. The checker ignores case, spaces, punctuation and accents, counts every letter in both entries, and shows which letters differ when they do not match.
Technically the same letters in the same order is not a rearrangement, so the tool tells you when both entries are identical.
No. Astronomer and moon starer are anagrams because only the letters count.
See also: palindrome checker · reverse text · word counter