If a defendant agrees to a settlement before the case is heard, is a "judgement" still signed by a judge?

Court Order = Court Order

What the court order says is what would dictate whether it is judgment or not.

If a defendant agrees to settlement, then it is possible to have what is known as Stipulated Judgment. A stipulated judgment contains provisions and settlement clause which parties have agreed to and will abide by. Judge sill sign it and only then it becomes order and judgment.