There are 3 types of real R4s:
1). White/Black shell with Teeth and a spring loaded MicroSD, no SDHC/DSi support.
2). Black shell without Teeth and no springloader, no SDHC/DSi support.
3). R4 RTS put out by the M3 Team after the original R4 disbanded.
R4's you buy now are 99.99% guaranteed to be fake, however you can buy 1:1 (one to one, or exact) clones that are supposedly put out by the R4li Team who supported the original R4 with a few (semi buggy) menu updates.
Because they are exactly the same as a real R4, they will work with everything that the R4 works with like the official builds of WoodR4.
R4's with SDHC, i, III, Upgrade, Renovation, Ultra, etc are all using the R4 name to sell their carts. No team other than M3 had ties to R4 or permission to use the R4 name. However, not all R4 clones are terrible.
The R4 Ultra is an AceKard clone, but it will not run an AKAIO newer than 1.8.1.
The R4i Gold and R4iDSN can run Wood and support SDHC and DSi (not sure if they support updatable firmware).