The emphasis is "as much value."
When 2 or more links are from websites hosted on the same C-Class IP address, they're often owned by the same person/company, and therefore are viewed as slightly less diverse than the same number of links from websites not hosted on the same C-Class IP address.
A C-Class IP is simply the third set of numbers in an IP address: AAA.BBB.CCC.DDD.
The only difference here is that these links are missing a bit of diversity, but they're not bad and they won't hurt you simply because of the IP address.
Regarding your clients' sites that link back to you - yes Google can tell that they're all hosted together. If you use a custom nameserver that's the same as your primary domain, you can bet they know you're related. Those links are less valuable than if those sites were all hosted on separate servers, but rather than moving all of those client sites I would look into alternative link building strategies, since footer links as credits for a web developer aren't going to be a sufficient strategy for all of your link building activity.