Does every data type just boil down to nodes with pointers?
Well, that is basically what all data structures boil down to. Data with connections.  The nodes are all artificial - they don't actually exist physically. This is where the binary part comes in.  You should create a few data structures in C++ and check out where your objects land in memory.  It can be very interesting to learn about how the data is laid out in memory. 

The main reason for so many different structures is that they all specialize in one thing or another. For example, it is typically faster to iterate through a vector instead of a linked list, due to how pages are pulled from memory.  A linked list is better to store larger sized types because vectors must allocate extra space for unused slots (this is required in the design of a vector).

As a side note, an interesting data structure you may want to look at is a Hash Table.  It does not quite follow the Nodes and Pointers system you are describing.  

TL;DR: Containers basically all Nodes and Pointers but have very specific uses and are better for something and worse for others.