C programming syntaxes for NXP LPC1768
This is elementary C programming has nothing to do with your microcontroller.

You can have a variable:

unsigned int jim;


and you can have structures

typedef struct
{
    unsigned int bob;
    unsigned int ted;
    unsigned int carol;
    unsigned int alice;
}  MYSTRUCT;
MYSTRUCT one;
MYSTRUCT *two;


In the case of one, we have asked the compiler to allocate the memory for that structure, it is compiled in basically not a malloc thing.  For the two case that is saying we have allocated a pointer only, the address to the structure, but the memory for the structure is not yet allocated. in the case of what you are seeing, they use the latter case then use C tricks to force the address of two to be a specific address, then we can know/assume that from that bob, ted, ... are known offsets, so if you have say a bank of uart registers, and there are 10 of them and they are 32 bits wide you could in theory define a 10 element structure of 32 bit variables tell the compiler you want that structure aimed at the beginning of that register bank and then by accessing elements within the structure you access those registers.  Or you could just make individual variables like the jim variable above and likewise point that at some location (during the declaration so that at compile time the address is forced).  There is more C syntax I am not showing to force the address, but using the variable defined above the syntax for those variations is as follows:

jim=5;
one.bob=5;
two-&gt;bob=5;


with a variable you just use the name if it is a variable within a structure then it depends on if the base name of the structure is a pointer or not, if not a pointer you use a dot between the structures base name and the variable within  one.bob, and if it is a pointer then you use an arrow  two->bob.  assume that one and two are not pointing at the same address so those are really two separate bob variables. 

What you are seeing is two different ways to approach the problem of creating variables that can be used at the address of a hardware register, and by using different declaration techniques you get the two styles you pointed out in your question.