They are very similar from a distance but there are easy ways to tell them apart.
Eupatorium perfoliatum - boneset- is generally a rougher looking plant, but you can really only tell that if you're very familiar with the two varieties or if they happen to be close to each other.
They're not going to be close to each other because their habitats are significantly different. Boneset likes open places and plenty of sun; White Thoroughwort likes shade.
Boneset is a taller plant. It gets about 36 inches tall if it's happy. The ones around here are typically 30 - 36 inches.
Tradition has it that boneset is called that because it was actually used to help bones heal.
Here are pics of boneset. White flowers. Look closely at how the leaves grow around the stem in the pic on the right. It looks like the stem is growing right through the leaves. Remember the Latin name - perfoliatum? That means 'through the leaves'. 'Per' = through. 'Foliatum' = leaves.
Now, here is the pic of White Thoroughwort. It's much daintier plant. They are shorter, from 18-24 inches around here.
Notice that the leaves are heart shaped. They are opposite [the pairs are opposite each other on the stem] but the leaves have stems and the main stem of the plant does not look like it's growing through the leaves at all.
Here's some more plant Latin for you. Album [or alba] = white.
And here's some plant Old English for you. Wort = plant. You'll see a lot of the common names for wildflowers have 'wort' in them. It's the Old English word, originally 'wyrt', for 'plant'. The theory is that it came from an even older Indo European word - wra:d.
Now you know.