Adam Clarke on Psalms 20:7

Some trust in chariots - The words of the original are short and emphatic: These in chariots; and these in horses; but we will record in the name of Jehovah our God. Or, as the Septuagint, μεγαλυνθησομεθα, "we shall be magnified." Or, as the Vulgate, invocabimus, "we shall invoke the name of the Lord." This and the following verse I suppose to be the words of David and his officers. And the mention of chariots and horses makes it likely that the war with the Ammonites and Syrians is that to which reference is made here; for they came against him with vast multitudes of horsemen and chariots. See 2Sam 10:6-8. According to the law, David could neither have chariots nor horses; and those who came against him with cavalry must have a very great advantage; but he saw that Jehovah his God was more than a match for all his foes, and in him he trusts with implicit confidence.