Equivalent 'extract by mask' tool in postgis

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Context: A large raster is clipped to create a bunch of smaller rasters based on a bunch of shapefiles.I've used st_clip() which seems to take forever looping through the different shapefiles, so I've switched to the much faster (but fast enough?) combination of 'where st_intersects()' and smaller tile sizes. The Extract by Mask tool on arcgis seems to be faster. Is there a difference in how they are both done? As I understand it, it rasterizes the vector shapefile and creates a matrix of 0s and 1s and extracts the values from the base raster which intersect with the 1s.



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