I would've thought ping and speed would go hand in hand.
No, that's why most speed tests report these separately.
ping requires a response from the server before the second half of the "round trip" can continue. So the
ping time is the sum of the upstream transmit time, time for the server to respond, and the downstream transmit time.
So would this suggest that the mobile connection is "further" from its destination, but "wider" and capable of higher throughput?
These signals travel at the speed of light, so the distance between source and destination would have to be very large before it's a factor. Your mobile phone is probably serviced by a tower within a few miles. Even a (low orbit) sat phone transmission is less than a thousand miles.
Almost all long-distance transmission schemes, including the two methods you are comparing, use serial transmission. They might employ a modulation schemes (digital information over analog channel) that transmits several bits per symbol (e.g. 3 bits for 8VSB or 8 bits for QAM256). But this is accounted for in the bits per second specification for the transmission rate.
You simply cannot infer request&response throughput performance based on unidirectional transfer rate. You need to account for server response time, the number of intermediate relays or hops that may occur (store & forward retransmissions that are fully buffered or cut through that add only a small delay) and protocol overhead.