There are 2 different types of modes in this context. In AH, through the ingame control mapping, there are 3 or 4 possible modes, allowing you to setup joystick scaling and other controls, so at the press of a button, you can change them around. As an example, I have the joystick, throttle, rpm, and rudder axes mapped through AH, and also the Reset button button on the throttle display. I have 2 modes set up in game, with no stick scaling for one, and scaling enabled on the second one. I use one for fighter, and one for buffs/gvs/gunning, to get a little smoother aiming.
In the Saitek software, when you've got the profile editor up, there's a menu bar that says "Shiftstate", and in the bar, it displays the Mode you're currently programming things in. Clicking on that bar lets you select different modes to program, and also the Shift modes (which let you use the pinkie switch as a shift key, instead of a button, effectively doubling the number of commands available without having to change modes or profiles). Might be easier to load my profile up in the editor and look through all of this than it is for me to explain. It accomplishes basically the same things as the AH mode, but has a little more flexibility (and more complexity) than the ingame programming.
Similar to the AH Modes, it allows for different button mappings to be loaded. These, you can toggle by using the rotary button with the LED on the top right of the stick. Just like the game, these can be changed at will by simply rolling the knob forward and back, with the LED changing colors, and the display on the throttle base also displays which Mode you're in (1,2 or 3).
I just checked, and the 1 reset timer button on the base is the only key press I have mapped through the game. It's not mappable in SST (since its dedicated to the MFD function) so I mapped it in game. None of my other stick buttons register in the game controls setup when I have a profile loaded. I'm not sure if you can double up the controls.
Anyways, when you're in the SST Profile Editor, when you get your commands where you want them, at the top of the screen, File, Save As, name it so you remember what it is, then hit Save. The modes in SST are part of the profile itself, so you won't have AH2profileMode1.dta, AH2profileMode2.dat, etc. You'll have the single profile with all 3 modes and all 3 shift stats, selectable with the twist of a knob, all in the same profile. This is different from the AH ingame programming where the different modes are the equivalent of different profiles. Hope this helps a bit.