Why do products of nuclear decay have a lower mass than the original nucleus, when the sum of the mass of its nucleons is larger?

I've just started covering the topic of binding energy in Year 13 at school (final year before University). The definition we've been given of binding energy is that it is the work done when separating a nucleus into its constituent nucleons. Alright so far.

We've also covered nuclear decays, and an example of that we've been given is

where the mass of the Thorium isotope and the alpha particle (constituent parts) is less than the mass of the Uranium isotope (I've checked this - it's true). We were told this was due to the combined binding energy of the products being less than the binding energy of the uranium isotope.

However, this seems to contradict examples I've found on the internet, such as the formation of an alpha particle from 2 protons and 2 neutrons (see here), where the mass of the constituent parts is higher - energy must remain constant, and the alpha particle has a higher binding energy, so the mass-energy must necessarily be lower. This makes sense.

If someone is able to give a clear explanation of why both of these things are true, I'd be very grateful!

Thanks