Is hard surfacing wire all the same?

Ah, so he is clueless.
Yes, there are many different types of hard surfacing electrodes. Each has its own range of uses.
Ah, so you're clueless too.
You can change the tip, but your machine is going to really be pushed to run that thick a hard wire.
I think you're setting yourself up for trouble here. You're attempting to do something you don't know how to do, and you're being asked to do it in a way that is almost certain to provide an unsatisfactory result.
Gary

0.045" hardfacing wire is actually a dual-shield process. There is a shielding gas and a flux layer left on the bead.
0.045" is the limit of a Millermatic 251. You will be running pretty hot. Make sure not to feed too much wire or you will get bad porosity.
I have run many pounds of 0.045" Rankin Ranomatic DDG and BBG for anvil surfaces.
The Rankin stuff was considerably cheaper than Stoody or UTP, and has worked great.

Yes you can change the tip to .045 Your machine will be at its limit but since you are only running one small bead it should be ok. The choice of wire and the application is unknown. If the bucket is being used on sand and earth you can have a relatively hard and brittle weld. If the bucket is going to be striking rock on a regular basis too hard a bead will fracture off. Some hardsurfacing will require preheat.. Generally hardsurfacing beads are run cold to limit dilution of the weld bead material with the parent metal. Yes there are a wide range of hardsurfacing consumables. The safest way is to ask the supplier for advice. Even that is not fool proof since there are many fools selling hardfacing materials. Ask for some product literature and take your chances. There have been many people who have been turned off hardsurfacing simply because they have used it in the wrong application or used the wrong wire.
Randy