In reply to KP_3030:
I couldn't see a reference to thunderstorms in the forecast you linked. The only medium hazard was strong sunlight (there's reduced ozone layer over the UK just now).
More generally, as Mark says, the area forecast is written by a human. This won't be based on just one model, but will consider a range of different of sources of information, including other models and observational data. The summit specific forecasts are generated from a mix of models and don't have any human input.
The other factor is that the way the symbols for the summit specific forecasts are selected is a bit complicated, but essentially looks at the likelihood of each different weather symbol, but with a weighting applied to favour more hazardous weather types.
If the area forecast is showing a medium likelihood of thunderstorms, but no thunder forecast in site specific forecasts I suspect the most likely reason would be it hasn't quite reached the threshold to be shown in the site specific, but the human forecaster has judged that the risk is significant enough to flag up.