Since you're still reading, you probably want to know how to determine EXACTLY what motherboard type your S model slim is. With relative reliability we can determine if you have a Trinity or a Corona simply based off the MFR date on the sticker at the rear of the console.
-Slim "S" Series consoles with a MFR date on the back of 07-2011 and BEFORE are almost certainly Trinity.
-Slim "S" Series consoles with a MFR date on the back of 08-2011 and AFTER are almost certainly Corona.
*If you are attempting to plan your RGH project, judging my the MFR date alone is reliable enough to order supplies for a Trinity console but if your MFR date falls into the date range of a Corona you will want to do further checking to determine what specific variation of Corona that you have. All Trinity consoles can be RGH'd with the same equipment, but Corona consoles vary from v1 through v6.
To tell with 100% certainty if you have a Trinity or a Corona, we really must open the console and have a look at it's motherboard.
The Trinity motherboard is easy to identify as it has two vertically oriented nand headers. It may or may not have the 4gb add-on.
If from this image you have identified you have a Trinity console, you can find a detailed Trinity RGH guide here.
The Corona motherboard is similarly easy to identify as it's left nand header is the same as a Trinity, but the right nand header is rotated 90 degress and is therefore sideways as compared to the Trinity.
If from this image you have identified that you have a Corona motherboard, there are actually several additional items that you should check to see if you will need a 4gb R/W tool or a postfix adapter. Click HERE to go to the page for additional info on Corona.