They're not different things and haven't been since the late 90s. All the big media companies have interconnects for CDN purposes; the only difference is that they pay for them (or have settlement-free peering arrangements). Peering disputes like this are as old as the Internet.

When the other party dumps their nice, CDN-backed delivery service in favor of cheap transit from a provider long known to have ~20% packet loss at peak hours, then complains loudly about it, THAT is fishy.

Many people seem to think of the Internet as a big hole that you can throw data into and it magically gets where it's going. Once you start pushing enough traffic, it's YOUR responsibility to ensure you traffic gets where its going, which means spending money on delivery.