The second definition could be a confusion of ownership — i.e. are you paying a CDN to do higher-level service or running the services yourself?
Wikipedia's definition primarily focuses on the local/IoT version as a distinctly different from utilizing a CDN.
https://en.wikipedia.org/wiki/Content_delivery_network contains
> Most CDN providers will provide their services over a varying, defined, set of PoPs [...]. These sets of PoPs can be called "edges", "edge nodes" or "edge networks" as they would be the closest edge of CDN assets to the end user"
There's also https://en.wikipedia.org/wiki/Edge_device which uses yet another idea of what The Edge is (in this case routers to a bigger network)