I think that on RSI simple you have simple smoothing, and on RSI wilder you have wilders smoothing. Normally on the normal RSI you have a 5-day EMA while on Wilder's RSI you have a 5 day wilders smoothing (which is similar to the EMA, it responds slowly to price changes compared to the EMA) I think thats what it is.
Wilder  invented the RSI indicator and presented it in New Concepts in Technical Trading Systems. His method uses a smoothing measure which reduces the noise in a signal but requires a decent amount of back-data before a sensible result can be got (to match the Bloomberg 9-day RSI you need 6 months of back data).
Some other places don't bother with the smoothing. Take, for example, interactive investor/Ample (www.iii.co.uk) who do away with the smoothing altogether and just show the basic non-smoothed numbers. More signals but perhaps less useful??
If you need it I'll post the Wilder method sometime, but you can probably find it in many places, I think I first saw it on the Equis pages.
 Welles Wilder, the author of the above-mentiond book.
an article for your thoughts......and for users of Metastock both the formulae...
In "The RSI Smoothed" in this issue, John Ehlers bases his calculations on an RSI calculation that sums the changes in the closing price. While some technical analysis programs use this version, Welles Wilder's book New Concepts In Technical Trading Systems defines the RSI slightly differently. Wilder smoothes the sums using his own averaging method before he calculates the final ratio. Since MetaStock uses Wilder's method of calculating the RSI, we are including both John Ehlers' formula, as presented in his article in this issue, and a formula for adding Ehlers' smoothing to the standard RSI.
To create an indicator in MetaStock, select Indicator Builder from the Tools menu, click New, and enter the following formula: