The optical band gap depends on the particle size, if the particle size change is in the order of magnitude of the Bohr Radius. According to literature, the Bohr Radius of CsPbCl3 is 5 nm, which means a difference in particle size in this range caused by the different coating technologies may also cause the difference in the band gap.
Since you didn't mention the film thicknesses, material quality (e.g., single crystalline vs. poly-crystalline), measurement technique, and how you analyzed the data, there are various possible reasons that could yield different bandgaps.
I suspect you probably used tauc-plot type analysis to get the bandgap. This technique tends to give ambiguous results, depending on the film thickness, the spectral range used for analysis, material quality, etc. See this paper for discussions: Article Comparative studies of optoelectrical properties of prominen...
Regarding the size effect, unless your film thickness is in the order of 10 nm or below, the quantum confinement induced bandgap change should be minimal.