In C, declaring your enum the first way allows you to use it like so:
TokenType my_type;
If you use the second style, you’ll be forced to declare your variable like this:
enum TokenType my_type;
As mentioned by others, this doesn’t make a difference in C++. My guess is that either the person who wrote this is a C programmer at heart, or you’re compiling C code as C++. Either way, it won’t affect the behaviour of your code.