I would say the information I found and the fact the carb is WT-3 confirms that you have the 38cc engine. I would run the engine with the carb you have assuming it is in good shape to get a baseline. You can get a rebuild kit for around 5 dollars or so. Then switch to a larger one and you should see a good gain in performance. Also, this carb has no choke per the Walbro Parts & Service Manual. When you do go to the bigger carb try for one with a choke. If you need a carb let me know, I have dozens and would ship you one for $15.00. I bought 200 of them from a guy that went out of business. Kept the ones that work for plane engines and scrapped the rest. As for sizes etc, the 13 mm or in your case the 9 mm is the size of the venturi on the side of the carb that fits to the intake manifold. The other side has a raised number cast into it. In your case it may be a 20 or 24. This is the size of the intake in 64ths of an inch. Thats about as simple as I can make it. The more you do the more you will understand. What does the engine weigh as it sits?

Tim