anyway vs at any rate

anyway and at any rate both are adverbs.

Word	Noun	Adjective	Verb	Adverb
anyway	No	No	No	Yes
at any rate	No	No	No	Yes

As adverbs, anyway and at any rate are synonyms defined as:

anyway and at any rate: used to indicate that a statement explains or supports a previous statement

Other synonyms of anyway include anyhow, anyways, in any case, in any event.

anyway (adverb)	at any rate (adverb)
used to indicate that a statement explains or supports a previous statement	used to indicate that a statement explains or supports a previous statement
in any way whatsoever	if nothing else (`leastwise' is informal and `leastways' is colloquial)