Albert Barnes Commentary Psalms 20:7

"Some [trust] in chariots, and some in horses; But we will make mention of the name of Jehovah our God." — Psalms 20:7 (ASV)

Some trust in chariots - This (see the introduction to the psalm) seems to be a “general chorus” of the king and the people, expressing the fullest confidence in God and showing the true ground of their reliance. The general meaning is that their entire trust was in God. This is put in strong contrast with others, who relied, some on their chariots and some on their horses, while they relied alone on God. Those who trusted in horses and in chariots would be overcome; those who trusted in God alone would triumph.

The word translated "chariots"—רכב rekeb—properly means riding, and then a vehicle for riding, a wagon, or a chariot. It refers here to the war-chariot, the vehicle for carrying armed men into battle.

These chariots provided great advantages in war because of the speed with which they could be driven against an enemy and the ease of fighting from them. They were usually very simple in construction.

They typically consisted of a light pole suspended between and on the withers of a pair of horses, its rear end resting on a light axle-tree with two low wheels. On this axle stood a light frame, open at the back, and floored for the warrior and his charioteer, who both stood inside. The war-bow, in its case, hung on the sides of the frame; a large quiver with arrows and darts commonly had a particular sheath.

“In Persia, the chariots, elevated on wheels of considerable diameter, had four horses abreast; and in early ages, there were occasionally hooks or scythes attached to the axles.” - Kitto, “Cyclo.” In early ages, these constituted a main reliance in determining the result of a battle.

And some in horses - This refers to cavalry, commonly a very significant reliance in war. The use of horses in war was known early in the world, as we find mention of them in the earliest periods of history.

But we will remember the name of the Lord our God - That is, we will remember God—the name, as previously remarked, often being used to denote the person. The meaning is, we will not forget that our reliance is not on armies, but on God, the living God. Whatever instruments we may use, we will always remember that our hope is in God, and that only He can give success to our arms.