杯子means “a cup”。杯could mean both “a cup” or “cup of sth” one more thing，you can never learn Chinese well by understanding each character separately， they all got several meanings in different phrases

杯 = counting word i.e a cup of something 杯子 = noun, a cup

一杯水 is right, means a cup of water; 一杯子水 is not right. 杯： quantifier. you can say 一杯/两杯/几杯。 杯子:noun, such as cup, glass. This 杯子 is pretty. where is my 杯子？ But, in some areas,especially the north of China, 杯=杯子，means cup/glass, for example, where is my 杯/杯子？ this is my 杯/杯子。I want to buy a 杯/杯子。

“杯” n.="杯子" cup n. “一个杯”or“一个杯子” it's a cup and it can be “一杯水” a cup of water but can not be "一杯子水"

same meaning