If you are having trouble tracing the definitions, you can use the preprocessed output of the compiler which will tell you all you need to know. E.g.
$ cat test.c
#include <stdio.h>
$ cc -E test.c | grep off_t
typedef long int __off_t;
typedef __off64_t __loff_t;
__off_t __pos;
__off_t _old_offset;
typedef __off_t off_t;
extern int fseeko (FILE *__stream, __off_t __off, int __whence);
extern __off_t ftello (FILE *__stream) ;
If you look at the complete output you can even see the exact header file location and line number where it was defined:
# 132 "/usr/include/bits/types.h" 2 3 4
typedef unsigned long int __dev_t;
typedef unsigned int __uid_t;
typedef unsigned int __gid_t;
typedef unsigned long int __ino_t;
typedef unsigned long int __ino64_t;
typedef unsigned int __mode_t;
typedef unsigned long int __nlink_t;
typedef long int __off_t;
typedef long int __off64_t;
...
# 91 "/usr/include/stdio.h" 3 4
typedef __off_t off_t;