兩者皆指「arm」，但胳膊通常指整條手臂，臂則可分上手臂(upper arm, i.e., below the shoulder and above the elbow)及下手臂(lower arm)。

I think normally 胳膊 refers to upper arm, and 手臂(you'd better say手臂）refers to the whole arm. for example,if there's cut in your upper arm, you could say, 你手臂怎么了？or 你胳膊怎么了？if there's a cut in your lower arm or any other part of your arm,you'd better say 你手臂怎么了？instead of 你胳膊怎么了？

在中文里边，胳膊比较口语化，臂比较书面化。说“臂”时常说“手臂”。

胳膊：arm 手臂：arm 手臂 is more offical. for example, in medical sience, u can meet "手臂" 臂：every thing which looks like "arm" can be called 臂 for example, 机械手臂/机械臂 for a crane as u konw, it has a long part. for this part we call it 机械臂