Are the Amorites and Arameans the same people?

They were not the same people.

Amonites were at peace with Israel during the time of Saul (David's time).

It is mentioned that in the days of Samuel, there was peace between them and the Israelites (1 Sam. 7:14). The Gibeonites were said to be their descendants, being an offshoot of the Amorites that made a covenant with the Hebrews; when Saul would break that vow and kill some of the Gibeonites, God sent a famine to Israel.

Arameans were at war with Israel during the time of Saul.

The Aramaeans were, in the 11th century BC, established in Syria. The Bible tells us that Saul, David and Solomon (late 11th to 10th centuries) fought against the Aramaeans kingdoms across the northern frontier of Israel: Aram-Sôvah in the Beq’a, Aram-Bêt-Rehob and Aram-Ma’akah around Mount Hermon, Geshur in the Hauran, and Damascus.

For the first time, an inscription of Tiglath-Pileser I (1115-1077 BC) refers to the "Ahlamû-Aramaeans" (Ahlame Armaia) and shortly after, the Ahlamû rapidly disappear from Assyrian annals, to be replaced by the Aramaeans (Aramu, Arimi). "Ahlamû-Aramaeans" would consider the Aramaeans as an important and in time dominant faction of the Ahlamû tribes, however it is possible that the two peoples had nothing in common, but operated in the same area.[2] It is conceivable that the name "Arameans" was a more accurate form of the earlier ethnonym Martu (Amorites, westerners) in the Assyrian tablets

No. The Amorites disappeared from the Middle East and then reappeared in Germany a many years later. They conquered and then intermingled with the Barbarians to become the Prussians of which Germany is one of the Prussian countries.

Not even close.