Mother had led me to believe the new baby was a kind of present for me.

Shawn was just dropping off a pair of new sneakers.

I picked up a piece of wood and started carving. 

请问老师：

a pair of/a kind of/a piece of到底是什么成分？我搜了搜其它的帖子有的把它们称为限定词，有的说不是限定词，有的把它们叫作修饰语/限定语，也有把它们叫作定语的，这些都是指的同一个意思吗？我应该采用哪种？因为了解的比较局限，对这部分知识实在是感觉乱，所以还辛苦老师具体解答一下，谢谢老师！