A lovely example：

支撑： 那段日子很艰难，一家人的生活全靠爸爸支撑。

八根柱子支撑着这座桥。

支持：生活中，我们需要朋友和家人的支持和鼓励。

他筹钱来支持慈善事业的做法让人尊重。

Maybe the differences are just like "put up","prop up"(支撑）against “supportive“ ,“support” and "hold your back"...（支持）. But in the mean time I think you are right about these two words：The first is more physical while the last one is more emotional.

支撑 is more like to have a point to support a view or actually have a point to lay on literrally，this is also more formal and for writing. 支持 is more emotional yes, like being supportive or something like that

支持和支撑都有勉强维持的意思。但是 ，支持一般都是心里感受，比如支持别人的决定。支撑是外界的，比如他双手支撑着身体从地上爬起来了。（总结:中文词汇意思有很多，主要靠语境去理解！）