The number of possible positions in shogi is much larger than in chess, mainly due to the unique feature of shogi where captured pieces can be reintroduced to the board by the capturing player. However, the numbers (10^120 for chess and 10^220 for shogi)that some sources give represent estimates of the number of possible game positions, not moves. 

For chess, the number of possible game positions is often estimated to be around 10^43 to 10^50, which is referred to as the "Shannon number." This number comes from a rough calculation made by mathematician and computer scientist Claude Shannon in 1950. It is important to note that these numbers are only estimates and should be taken with caution.

In the case of shogi, the number of possible game positions is not as well established, but some estimates suggest it might be around 10^71 to 10^198. This wide range is due to the uncertainty in estimating the complexities of the shogi rules and the impact of piece drops. Again, these numbers are estimates and should be interpreted with care.

Despite the uncertainty in the exact numbers, it is true that the number of possible positions in shogi is much larger than in chess, making it a more complex and challenging game. This complexity arises from the ability to capture and reuse pieces, which leads to a vast array of potential board positions and strategic possibilities. As a result, shogi games tend to be longer and more difficult to predict compared to chess games.
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