always use foreign keys to store referential records, that is userID in your case.
and regarding the approach on how to store, it depends on what you need.
a) if you want to know who last updated the record. then you should
create a userID
column in the table.
it is always good to store foreign keys instead of other records, because this way you can relate and fetch all the records of a user. this approach will have a limitation though, since you can store only one userID, you can only know who last updated it.
b) if you want to store all the records, to know which user updated
the records and when, then you should store it in one to many
relationship table. for example
user_log with columns user_id, update_datetime
and perhaps a message column, telling what did the user do.