The first mower has the two-stage air cleaner which was fitted to the I/C engines and some others. The second one has the standard, single-stage air cleaner. What makes you think the second engine should be fitted with the two-stage? Incidentally, you can see that the second engine has a different cooling air intake grille as well as a different air cleaner.
You have not given the model or type numbers for the second engine. Here is the illustrated parts list for the first, probably older engine - the 110908 0418:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6lnsHVJ1DajI.pdfAs you can see, it shows both types of air cleaner.
