Weather agency's predicting opposing weather?

Meteorologists don't really predict the weather. From all worldwide present observation, collected then redistributed by the World Meteorological Organization, national authorities feed those into big computer models that come out with a prediction. There might be a different output from say, American to British models, at long range, but it is pretty much similar for the next 24 hours. You can check that e.g. on weatheronline.co.uk, then selecting "Expert Chart" and see the different models available.

But a local meteorologist will tend to add local knowledge. For example the met officer at an airfield will guess that, during a high pressure with little wind and clear sky, early morning fog patches can be expected nearby the airfield.

If say, a frontal low pressure is moving in from the west, the forecast is quite certain: it will be rain and wind. It can't be otherwise; the low pressure can't just vanish like that. Perhaps the timing might be wrong and the rain comes a few hours earlier or later than predicted but ... it will come.

Other things like, thunderstorms, are very unpredictable. All we can say is that we measure the air to be unstable and the moisture to be high. Those are ideal conditions for thunderstorms but, will it happen or not? difficult to say.

Depending on the type of weather report, agencies my give the percentage of probability or simply say what they think will happen. If the latter, it may be that two different persons have two different ideas.