Among the Japanese phraseological units, there are many synonymous:
一石 二鳥 /isseki-nicho:/ (lit. two birds with one stone)
一挙両得 /ikkyo-ryoku (lit. double benefit with one stone)
to kill two birds with one stone.

Sometimes phraseological units are identical in their meaning, stylistic and syntactic functions, but differ in a certain lexical component or grammatical form:
昨日は 昨日、今日は今日/kino: wa kino:, kyo: wa kyo:/ (lit. yesterday is yesterday, and today is today)
昔は昔、今は今 /mukashi wa mukashi , ima wa ima/ (lit. earlier then earlier, and now - then now)
what was is gone, but you have to live today.

Sometimes phraseological units are similar in structure have different meanings, for example:
猿も木から落る/saru mo ki kara ochiru/ (lit. and the monkey falls from the tree) a horse on four legs, yet it stumbles
木から落きた猿/ki kara ochita saru/ (lit. a monkey that fell from a tree) like a fish pulled out of water (a state of confusion and helplessness).

Rarely one phraseological unit has different meanings, for example:
帯を解く/obi-o-toku/
(lit. untie the belt of the obi)
1) surrender (to a man);
2) calm down.

Also there are phraseological antonyms that have opposite lexical meanings, but the same lexical-grammatical characteristic:
狐、その尾を濡らす/kitsune, sono oh-oh nurasu/
初めよければ終りよし/hajime yokereba owari yoshi/
easy beginning easy and end.

What idioms do you know? Share in the comments!