Hi,
Definitely not a stupid question!
There could be all sorts of reasons for the delay, all of them would be due to implementation of the streaming, rather than with any failure of the devices!
I suspect the biggest difference may be down to the cache size of each device.
A very simplified description could be; the stream will be downloaded to memory (the cache) within the device first - when the cache is filled, the stream will start playing.
If there are any errors with the stream, the music will keep playing (using the stored data within the cache), while the section with errors is re-downloaded.
The larger the cache, the less likely there will be breaks, or errors in the audio you hear!
I hope that makes sense!
EDIT:
Ahhh, just re-read your question! DOH!
One will be served by the almost live DAB radio system, with a small delay for encoding, broadcasting, decoding and caching etc. (When compared to FM, for example).
The stream to Alexa isn't broadcast by radio. It will have further delays due to the encoded broadcast being passed around a number of servers, before ending up at your internet router and then sent by WiFi to your Alexa!
That can all create quite a large delay!
And that delay can vary, depending on differing server loads!