Is there any difference between ways of counting Borda?

I've heard of three different ways to count Bordalike ballots
 "each one receives n – 1 points for a first preference, n – 2 for a second, and so on"
 "As Borda proposed the system, each candidate received one more point for each ballot cast than in tournamentstyle counting, eg. 4321 instead of 3210"
 Sum up the rankings themselves and elect the candidate with the lowest sum
I've always assumed these are exactly equivalent, and will always elect the same candidate with a given set of ballots, but I want to make sure I'm not missing something. Are they the same even in cases where incomplete rankings are allowed, and in cases where equal rankings are allowed?

Well, it partly depends on what you do with equal ranks or incomplete ballots. If an unranked candidate is scored as 0 then a 4321 system would be different from 3210. But if it's done in a more sensible way, they would be equivalent.