Honda transmissions have traditionally shared one thing in common with manual transmissions: A single parallel shaft (countershaft) with constant mesh gearing. Outside of that, they are totally different beasts.
Where a shift fork would actuate a synchronizer in a manual transmission, Honda transmissions have a multi-plate, hydraulically actuated and lubricated clutch pack, very similar to the type used in a typical planetary automatic transmission. Honda transmissions still have sprags (one-way clutch) and overrun clutches, like their planetary cousins. Of course, Honda automatics all use a torque convertor as well.
Now, if you want to compare it to a *true* "self shifting manual", you'd have to look at a sequential manual gearbox (SMG). An SMG has all the same parts as a manual transmission: Single dry clutch, single parallel countershaft, synchronizers (or dogs), and shift forks. What it adds is an electro-hydraulic component that, simply put, shifts itself. When it's time to shift, the actuator for the clutch activates (which would be the same as you pressing the clutch pedal), the appropriate actuator moves the appropriate shift fork/synchro (as if you were moving the shift lever), and the clutch actuator releases the clutch (like you were letting off on the clutch pedal). All the motions are the same, except a computer is controlling some electrical actuators in place of your left leg and right arm.
side from a torque convertor and parallel shaft gearbox with dog-clutch gear engagement, it has two multi-plate clutches and a sprag clutch. It seems to have all the parts for an early dual clutch gearbox.
When you say "two multi-plate clutches", you have to look at where those clutches are located. On a dual-shift gearbox (DSG), the clutches control the connect and disconnect of the engine at the input shaft, like a traditional manual gearbox clutch would. In a Honda automatic, those "multi-plate clutches" are located in place of a synchronizer (which itself is a type of clutch). It "clutches" a specific power flow through the transmission, just like a planetary automatic does. The 6-speed GM auto in my Equinox also has two "multi-plate clutches" in it. That doesn't make it a DSG.
So, a DSG literally has two clutches. Why does it need two clutches? This is the really important part: A DSG has two clutches because it's has two input shafts! The input shafts are an shaft-within-a-shaft arrangement and each of the two clutches are splined to one of them. Why does it need two input shafts? Another important part: Because it has two parallel countershafts! One countershaft will house all the odd-gears, the other will have even. So, you have one clutch, input shaft, and countershaft for odd gears and another clutch, input shaft, and counter shaft for even gears.
Following the power flow: With first gear selected, clutch 1 (C1) is engaged and clutch 2 (C2) is disengaged. The odd and even shift actuators have 1st gear *and* 2nd gear engaged. Because there are two input shafts and C2 is released, no torque is being transmitted through the second input shaft.
When it comes time to shift, C2 is applied while C1 is released. That's it. 2nd gear was already preselected and torque is now being transmitter to the second countershaft. With C1 released, the odd actuator will transition from 1st to 3rd (this is done by moving a shift fork, just like a manual). Again, with torque going through the first input shaft, odd gears are free to move about at will. When it comes time to change gears again, C1 is applied while C2 is released... and so on. Because the next gear for each upshift is preselected, there is no time wasted actuating anything except the clutches during a shift.