I tend to be really bad at interchanging my words when it comes to cleansing and purification and I've come to realize that I probably shouldn't. So to clarify why this is probably not the best thing to do, I'd like to emphasize the difference between these words in the Craft. The textbook definition for both of these words are as follows:
Cleanse - clean, especially: to rid of impurities by or as if by washing
Purify - to make pure: as
a: to clear from material defilement or imperfection
b: to free from guilt or moral or ceremonial blemish
c: to free from undesirable elements
These definitions were taken from the Merriam-Webster Dictionary. As you can see, there is some difference in these definitions just as there is a difference in these words to the Witch. So by my definition as a Witch, cleansing is the process of physically cleaning your sacred space. Sweeping the area, mopping, dusting, raking leaves, etc. When you are cleansing an area, make sure to clean it to your best expectations. If you feel you haven't cleaned the area enough to welcome sacred deities into the space then continue cleaning or wait until you have time to clean the area properly.
Purification is the ritual or ceremonial act of ridding your sacred space of negativity. This is the type of work you do when you are smudging the area with sage or using the elements to protect your space.