would like, could like

Would like可以表示想要
后面跟动词不定式to do something
也可以说Would you like ......?表示委婉的请求或提出建议这时也可以用
Could like后面直接加doing something

would like + to do sth

could like + doing sth

would like to do sth=want to do sth=feel like doing sth

could like就是可能喜欢吧 - =|||.....

都一样，没什么区别，主要是喜好问题。