The difference is quite large, actually.
PTC is Pay to Click
This is when the network is looking for its users to click on ads to be paid - incentive based clicking. These type of networks typically don't last long as the model, quite frankly, doesn't work. Advertisers that do participate quickly realize that while they may be getting a lot of clicks for a low amount per click, the quality of the traffic is poor. Consider the mindset of the person viewing the ad: they are looking to make money by clicking on the ad more so than what the advertiser is offering, no interest in the advertisers offering. The long term effect is a one-off advertiser that will never return or continue advertising on your system.
PPC is Pay per Click
This is where the advertiser is paying on a per click basis. This, however, is where the similarity ends (for reputable networks) as incentive based clicking is not supported. Reputable PPC sites will randomly and routinely audit traffic for quality. Advertisers that utilize a reputable network will see fewer clicks at a higher cost per click with some of those clicks converting to an action (purchase, subscription, etc). The better PPC's will also include some form of conversion tracking as well, be it post click or post view. The problem is that many small networks have little to no real safeguards in place to stop click-fraud from occurring, let alone handle any significant traffic volume (use of cheap scripts). When selecting an advertising platform, these are two things you definitely want to look out for. In the case of PPC, advertisers should see conversions and likely renew or continue advertising on your network since they are getting real results.
Disclosure: As you can see from my signature, I am involved with a platform that does the latter of the two models. I do suggest looking around to see what is available to make an informed decision.