Why are there differences between Airbus and Cirium annual order totals?

The reason for differences between Airbus and Cirium annual orders totals is that Airbus use a different approach to how they present the data. 
 
When a type swap is announced for an On Order aircraft, Cirium labels the original order record as a Type Swap (think of these the same way you would order cancellations) and creates a new order as at the date of the type swap announcement. Airbus does not cancel the original order, and so retains the original order date for the aircraft (despite it being swapped to a new type). This means that when analysing gross and net orders (and order cancellations) for a specific period (e.g. over a year) there are sometimes differences in the totals. This particularly affects the A320 family where type swaps between the A320 and A321 are a regular occurrence. If you analyse the order backlog at any point in time and compare to Airbus, e.g. all A320 family aircraft with Status = On Order, or count the total net orders placed (at a point in time or all time), then our numbers will match those published by Airbus (we cross-check our data with the airframe manufacturers' on a monthly basis).
 
The recommended approach to match the Airbus order accounting methodology in a given year is to run an Aircraft Events - Summary search with the specific Order Event filters as shown in the screenshot below. For 2022, the total (gross) number of A320 Family orders placed = 888 (matching Airbus).

You can also separately search for Cancellations and from that work out the net orders. For 2022, Net Orders are 888 Gross - 118 Cancelled = 770 (matching Airbus).