開圖 is right. Both of them have several meanings used in different contexts. Except for the usages he pointed out, I thought of another one. "一个随意的人“ vs “一个随便的人” In this case, they are both used as adjectives. However, they have totally different meaning and sense. 我是一个随意的人，saying I'm easy going. 他是一个随便的人，indicating probably he always has casual relationships with many women and never be serious to any of them, kind of negative.

Sometimes they have the same meaning, but somtimes not. 1.我只是随便(随意)逛逛 they both mean not really serious,without destination or not really have to do it but you are doing it. 2.A:今天晚餐吃烤鸭好不好? B:随便(It's up to you) It can be impolite sometimes .we don't use 随意 to express that. 3.随便坐 in this situation we don't use 随意 often.It means that to do something in the way you feel comfortable. 4. if you say someone do something 随随便便,it means the one do the thing casualy or randomly.But no one says 随随意意 in Chinese nowadays. 目前我想到的就是这样了 加油 你的中文很好

意思是一样的。 言辞上”随意“文雅一些。 口语中”随便“经常用~

随意:是指根据自己心里所想去做,是自己的意识( suit oneself ); 随便：是指无所谓是什么,由别人来决定的行为。

What's more. as you go and visit your friend's house, you are invited in and then the host says to you"您随意，别拘束，就像在自己家一样" ，just like help youself in English. And in this situation, you can't use"随便".