Thule make the Halfords bars and boxes. They are just a lower spec (older models).
If you are only going to use them once or twice a year then I suggest going for the Halfords ones. If you are going to use them a lot then I’d go for for the Thule. Thule tend to be much quicker to take on / off. The wing bars are also much quieter and save on fuel – something you should definitely consider if you are planning to leave them on the car.
The other advantage of the thule stuff is you can use the t-bolt fittings on their cycle carriers and roof boxes.
Yes the bars and boxes are interchangable. When I worked at Halfords I usually recommnded Thule bars with Halfords boxes.
The Thule boxes a quicker to fit, are slightly more secure and open both sides. However, I would never leave anything valuable in them anyway as they are easy to break in to regardless of the brand.