$ file /bin/bash /bin/bash: ELF 32-bit LSB executable, Intel 80386, version 1, dynamically linked (uses shared libs), stripped
$ stat /bin/bash File: "/bin/bash" Size: 316848 Filetype: Regular File Mode: (0755/-rwxr-xr-x) Uid: ( 0/ root) Gid: ( 0/ root) Device: 3,66 Inode: 16213 Links: 1 Access: Fri Oct 5 21:11:48 2001(00000.00:01:26) Modify: Sun Feb 27 13:44:41 2000(00586.06:28:33) Change: Fri Dec 15 23:42:05 2000(00293.20:31:09)
Here's what the UNIX man page on stat has to say about the difference between a file change and a file modification:
st_mtime Time when data was last modified. Changed by the following functions: creat(), mknod(), pipe(), utime(), and write(2).
st_ctime Time when file status was last changed. Changed by the following functions: chmod(), chown(), creat(), link(2), mknod(), pipe(), unlink(2), utime(), and write().
So a modification is a change in the data, whereas a change also happens if you modify file permissions and so on.