Manufacturing grid determines the minimum dimension that can fabricated by that particular process of foundry. Please note , this is not the min length of transistor. For Eg : if manufacturing grid is 0.0001 for a process , then all the dimension of shapes should be a multiple of this. hence you cannot have shape with dimension (for eg say length ) as 0.00015 or 0.00017
Routing grid is normally the grid which has to be followed during P&R for various metal layers. usually due to various DRC constraints , Routing grid will be an multiple of Manuf grid.
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