Some trust in chariots, and some in horses: But we will remember the name of the Lord our God.” (Psalm 20:7, KJV 1900)

A more literal translation of this verse would be: “Some in chariots, and some in horses; But we will remember the name of the Lord our God.”

The ESV replaces “remember” with “trust,” even though the word does mean “to remember.”  I assume they did this because they felt that the  context better suited a translation of “trust.”

The Hebrew word here means “to remember, think about, consider, think on.”  I like to think of the verse in this way: While those who are not followers of the Lord are planning and relying upon the number of their chariots and the strength and size of their cavalry force for victory, those who follow the Lord do not do so.  Rather, they/we are thinking about, remembering, planning on, and trusting in, the Lord and his strength.

William Plummer comments:

Vain is the confidence of all wickedness.  In war, chariots, horses, navies, numbers, discipline, former successes, are relied on; but the battle is not to the strong.  “Providence favours the strong battalions” may sound well in a worldling’s ear, but neither Providence nor the Bible so teaches.