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When the GDAL based Interpolate function is run, the GDAL command generated does not match the parameters chosen in the tool dialog:

The attached screenshot shows the menu based Raster > Analysis > Grid (Interpolation)... dialog configuration. This is using the IDW interpolator with output in GeoTIFF, however the command line generated is as follows:

gdal_grid -l BathyODN_BNG -a invdist:power=2.0:smothing=0.0:radius1=0.0:radius2=0.0:angle=0.0:max_points=0:min_points=0:nodata=0.0 -of GMT C:/Local/Advanced_QGIS/Exercises/Data/Vector/Bathy/BathyODN_BNG.shp C:/Local/BathyInterp_InvDist.tif

Note that the smoothing parameter is misspelled, and also the output format (-of) is set to 'GMT', not 'GTiff' as requested. The latter generates an error when the tool is run.

When the same command is executed through Processing GDAL/OGR > [GDAL] Analysis > Grid (Inverse distance to a power), the same smothing -> smoothing typo is present, and the GDAL '-of' parameter is omitted entirely, meaning that a GeoTIFF is always generated regardless of the format and extension chosen in the dialog.