I'd say even the second meaning of rely on is interchangeable with depend on.
See here:
1. To rely, especially for support or maintenance:
Children must depend on their parents. 2. To place trust or confidence:
You can depend on his honesty. Source
Rely implies complete confidence, whereas depend implies confidence in the help or support of others.
Consequently, rely is more general, more "comprehensive" than depend.
Regards,
Snowcake