There are a few things you probably noticed in the previous examples that need explaining. The gint, gchar, etc. that you see are typedefs to int and char, respectively, that are part of the GLib system. This is done to get around that nasty dependency on the size of simple data types when doing calculations.
A good example is "gint32" which will be typedef'd to a 32 bit integer for any given platform, whether it be the 64 bit alpha, or the 32 bit i386. The typedefs are very straightforward and intuitive. They are all defined in glib/glib.h (which gets included from gtk.h).
You'll also notice GTK's ability to use GtkWidget when the function calls for a GtkObject. GTK is an object oriented design, and a widget is an object.