表达需要有听众，表示可以没有听众。

Although there are more detail in the differences, but for simplicity, 表示 is close to express 表达 is close to represent

“表达” is a vreb witch its subject is one's speaking, writing or action. It means that thing express one's emotion and feeling . You could say: 1.他的演讲表达了他的爱国之情. 2.他的文章表达了他对爱人的思念. 3.工人的罢工表达了他们的不满情绪. “表达” can be used as a noun too. It means one's expression, e.g. , "他的表达有问题(what he say is unclear.)". “表示” can be used as a verb or a noun. When it is a verb, it means someone show what his/her is thinking or what he/she wants to do. As its subject is a object or some kind of situation, it means that object is indicating something. Here are some examples: 1.他表示很难过(Emotion, but subject is a man). 2.这次的事件我表示无法理解(It is not showing one's feeling). 3. 他表示很感激. When it is a noun, it is some kind of action later. 1, 今天我生日,你有什么表示? Hope it could help.