Builtin nodesA builtin Overflow node is written in C++ and is part of the Overflow code (or compiled in an Overflow toolbox, like Matlab's mex files). In Overflow, all nodes are implemented as a class that derive (directly or indirectly) from a base class called "Node" (note that most nodes derive from "BufferedNode"). Although the Overflow implementation of different nodes uses C++ inheritence mecamism (using classes), there's no reason for the user to be aware of that. For that reason, it's not recommended to refer to nodes as "types" (eg. if Overflow were written in C, nodes would be implemented as functions).
Subnets (composite nodes)An Overflow subnet is a collection of connected nodes that can be used as if it were a single node. Most Overflow subnets will be saved into .n files, which are almost the exact equivalent of Matlab's .m files. There's no real C equivalent because C is a compiled language (although it could be seen as a C function calling other C function).
Node inputs/outputsThe inputs of an Overflow nodes are equivalent to the arguments to a Matlab/C function. The same for outputs, while C is restricted to one return value, Overflow and Matlab can have several outputs.
Node parametersOverflow node parameters are also equivalent to C/Matlab function arguments. The difference between node parameters and node inputs is that the parameters cannot change at run-time. It is chosen at "build-time" and stays constant throughout the run. For instance, the "Constant" node has no input, but has a parameter called "VALUE" that is returned as the output of the node. Using constants, you can always "transform" another node's input into a parameter. The reverse is not true, however. Why then have parameters and not define every argument as an input? Simplicity and run-time performances. Sometimes, it's just a lot easier to know certain arguments in advance and be sure that they don't change during the run. However, when possible, it is better to implement arguments as inputs, as this allows more flexibility.
Right now, the only way to define a new type in Overflow is by adding C++ code for it in a toolbox (or the core). Eventually, there will (could?) be a way to pack data in a "struct" using Overflow nodes, but this is not implemented yet.
Some Overflow Nodes expect a certain type of data as input/parameter and will generate a run-time exception (which will abort execution) if the wrong data type is used (eg. a Load node expects a Stream as input and nothing else). Some nodes, like the NOP (no-op) node, can take any type as input. Some node have more complex behaviour, like the Add node that can add two floats, two Vectors of the same dimension, but cannot add a Bool and a Vector.
Now, why going backwards like that? That's a bit long to explain. The quick answer is "because". The longer answer involves faster handling of dependencies, faster processing, buffer management and things like that.