Radial Internal Clearance
Bearing internal clearance is defined as the total distance through which one bearing ring can be moved relative to the other in the radial direction (radial internal clearance) or in the axial direction (axial internal clearance).
It is necessary to distinguish between the internal clearance of a bearing before mounting and the internal clearance in a mounted bearing which has reached its operating temperature (operational clearance).
The initial internal clearance (before mounting) is greater than the operational clearance because different degrees of interference in the fits and differences in thermal expansion of the bearing rings and the associated components cause the rings to be expanded or compressed.
C3 Bearings Summary
The bore, diameter and width of C3 bearings are identical to the none C3 version.
C3 are exactly the same quality but have a different a purpose.
C3 bearings have additional internal radial clearances to allow expansion in high speed / temperature environments.
Typically suited to hot and high speed environments ( fans, high speed motors etc)
They can feel loose until at running temperature and speed.
They are unsuitable where critical alignment is required from the onset..
Unless the bearing you are replacing specifically says C3 on it then you should not replace it with a C3 bearing.
A rule of thumb is to replace like for like, there is no advantage to a C3 bearing in place of a standard bearing.