import glob
import shutil
import os

#=========List of items
list = ["cat size","house size","car size"]

#=========directories
FromDir = "H:/New/1RecievedFiles/"
CopyDir = "H:/New/2CopyTo/"

#=========get list of items to be used in glob.glob
filesList = [x.replace(" ", "*")+"*.*" for x in list]

#=========get list of new files in FromDir, use filesList in glob.glob
listOfNew = [glob.glob(FromDir+item) for item in filesList ]
# returns [['H:/New/1RecievedFiles\cat.size.txt'], ['H:/New/1RecievedFiles\house.size.fromBob.txt']]

#=========make a single list from the list in a list
listOfNewfiles = [item for sublist in listOfNew for item in sublist]
# returns ['H:/New/1RecievedFiles\cat.size.txt', 'H:/New/1RecievedFiles\house.size.fromBob.txt']

#=========copy files
[shutil.copy2(item, CopyDir) for item in listOfNewfiles]

$ ls -1
copyto/
car.size.txt
cat.size.txt
house.size.fromBob.txt

import os, shutil
# lst not list -- naming it list overshadows a builtin
lst = ['cat size', 'house size', 'car size']
# PEP8 - lowercase with underscore here; CamelCase for classes
from_dir = os.path.abspath(os.path.expanduser('~/test'))
copy_dir = os.path.abspath(os.path.expanduser('~/test/copyto'))

to_copy = [f for f in os.listdir(from_dir) if os.path.isfile(f)]
# ['car.size.txt', 'house.size.fromBob.txt', 'cat.size.txt']

for filename in to_copy:
    needle = ' '.join(filename.split('.')[:2])
    if needle in lst:
        dest_dir = os.path.join(copy_dir, needle)
        os.mkdir(dest_dir)
        shutil.copy2(os.path.join(from_dir, filename), dest_dir)

copyto:
car size/
cat size/
house size/

copyto/car size:
car.size.txt

copyto/cat size:
cat.size.txt

copyto/house size:
house.size.fromBob.txt

import os,shutil

for item in list:
    if 'cat' in listitem:
        shutil.copyfile(source, 'H:/new/2CopyTo/cat size/')
    elif 'house' in listitem:
        shutil.copyfile(source, 'H.......etc etc
    elif 'car'.....