Commit your work to the LORD, and your plans will be established. -Proverbs 16:3
The heart of man plans his way, but the LORD establishes his steps. -Proverbs 16:9
It is an abomination to kings to do evil, for the throne is established by righteousness. -Proverbs 16:12A quick lookup in Strong's confirms that these three verses do indeed use the same word, which is actually transliterated "koon" in Strong's (I just said "coon" 'cause I knew it would make ya look!) and rendered "established/es" in the ESV. It would appear to be another example of the ESV translator/editors trying to represent things that could be seen as textual parallels to reflect that in English; the RSV (upon which the ESV was based) uses "directs" in verse 9.
It is interesting to think of all three of these verses in the sense of something being "established" or "set up." We don't normally think in terms of our "steps" being set up and established like a monument for all time, but since we know that time doesn't really mean the same thing to God that it means to us... He sees the end, the beginning, all of it at once... every step we take does stand as kind of a memorial to God. Each one is there before we take it, and each one remains after we are gone. Now THAT's a sobering thought!