based on a discussion at the 2020 virtual UC

move_tifs.py

layer = 'grid' # if running this script outside of ArcGIS, this should be a full path to a feature class, not a layer name
fields = ['ID'] # this is field which matches the .tif filename

tif_folder = r'c:\my_tifs'
out_folder = r'c:\output'

with arcpy.da.SearchCursor(layer, fields) as cursor:
    for r in cursor: # for each row in the layer:
        print(r[0]) # print the ID
        tif_file = os.path.join(tif_folder,r[0]+'.tif') # get the path to the matching .tif file (c:\my_tifs\01234.tif)
        tif_destination = os.path.join(out_folder,r[0]+'.tif') # set up the path to copy it to (c:\c:\output\01234.tif)
        arcpy.Copy_management(tif_file,tif_destination) # execute the copy tool
        # this will repeat for each row in the input feature class