Moving data between tables in different tables in postgreSQL on other column

Question

I have a table in a schema called fs in a postgreSQl database that looks like this:

id  cik    tf_dict_phrase  factset_entity_id  key_name 
1   738076                 000BFD-E           raw_text/738076_2005-08-05_10-K
2   738076                 000BFD-E           raw_text/738076_2006-08-11_10-K
3   738076                 000BFD-E           raw_text/738076_2007-07-31_10-K

And I have another table in the public shema which looks like this:

id  tokenized  key_name
1   {"a":1...} 1000180_2005-03-18_10-K
2   {"b":1...} raw_text/1004980_2007-02-22_10-K
3   {"%":1...} raw_text/1004980_2006-02-17_10-K

I would like to fill in the tf_dict_phrase column in the first table with the data in the tokenized column from the second table based on key_name matching.

Do I need to turn key_name into a foreign key? Thank you!

The id's are autogenerated in each table, so they will not match necessarily.

Update: I tried this with no luck

UPDATE ten_k_with_public
SET    tf_dict_phrases = public.raw_document.raw_data
FROM   public.raw_document
WHERE  fs.ten_k_with_public.key_name = public.raw_document.key_name