Both “throughly” and “thoroughly” appear in the Bible.
The words cannot be synonyms, because if they just mean the same thing, then why use two different “spellings”? But clearly there is some distinction in meaning. We find the distinction by two methods:
1. Examining all the places each word is printed using a standardised, pure edition.
2. Then examining dictionaries/records.
From the Scripture we can see that THROUGHLY means fully/completely, and that THOROUGHLY means to have gone through, like as a process that penetrates or accomplishes an exacting going right through.
OED -> Throughly. 1. Fully; completely; perfectly. 2. Through the whole thickness, substance or extant; through, throughout, all through, quite through. And a subcategory meaning to that, Through, from beginning to end; for the whole length or time; all through.
OED -> Thoroughly. 1. In a way that penetrates or goes through; right through, quite through. 2. In thorough manner of degree; in every part of detail; in all respects; with nothing left undone; fully, completely wholly, entirely, perfectly.
It used to be said by KJBO advocates that “throughly” meant “fully specifically through the inside as well as the outside” while “thoroughly” meant “generally fully through”. These old definitions were not rigorously correct.
If you take the first definition from both entries of the words from the OED, it will explain everything, and make sense as to why these are two separate words with separate meanings.
Simplistic definitions as given by others abound, who make “thoroughly” mean “completely” while “throughly” is like an archaic-sounding form to mean “in a through manner”. While they are right to detect as difference, I expect the Bible is actually using the words in the opposite way, with “throughly” meaning fully or totally, while “thoroughly” seems more methodical or exhaustive.
There are people who try and say that these two words mean the same thing. While it is true there are very close similarities in both spelling and meaning, they are not the same thing. I also think that definitions given in the past, being not looked at properly, could give rise to people saying that such things are wrong, or that there is no distinction after all. That is why I have supplied the above, to go some way to begin to show that there is a clear distinction.
Furthermore, spellings in old KJBs have varied, but that doesn’t mean that spelling doesn’t matter or that the words are identical at all. Lack of standardised English orthography, typographical errors, etc. are all possible factors. We know that the way it is now is correct, but these matters were not always so precise, when we begin from 1611 or from Tyndale.