According to Chapter 9 (Parser and Optimizer), Page 172 of the Book Understanding MySQL Internals by Sasha Pachev

here is the breakdown the evaluation of a query as the following tasks:

• Determine which keys can be used to retrieve the records from tables, and choose the best one for each table.
• For each table, decide whether a table scan is better that reading on a key. If there are a lot of records that match the key value, the advantages of the key are reduced and the table scan becomes faster.
• Determine the order in which tables should be joined when more than one table is present in the query.
• Rewrite the WHERE clauses to eliminate dead code, reducing the unnecessary computations and changing the constraints wherever possible to the open the way for using keys.
• Eliminate unused tables from the join.
• Determine whether keys can be used for ORDER BY and GROUP BY.
• Attempt to simplify subqueries, as well as determine to what extent their results can be cached.
• Merge views (expand the view reference as a macro)

On that same page, it says the following:

In MySQL optimizer terminology, every query is a set of joins. The term join is used here more broadly than in SQL commands. A query on only one table is a degenerate join. While we normally do not think of reading records from one table as a join, the same structures and algorithms used with conventional joins work perfectly to resolve the query with only one table.

EPILOGUE

Because of the keys present, the amount of data, and the expression of the query, MySQL Joins may sometimes do things for our own good (or to get back at us) and come up with results we did not expect and cannot quickly explain.

I wrote about this quirkiness before

• Jan 23, 2013 : Problem with nested UPDATE queries
• Feb 22, 2011 : Problem with MySQL subquery

because the MySQL Query Optimizer could make dismiss certain keys during the query's evaluation.

@Phil's comment help me see how to post this answer (+1 for @Phil's comment)

@ypercube's comment (+1 for this one too) is a compact version of my post because MySQL's Query Optimizer is primitive. Unfortunately, it has to be since it deals with outside storage engines.

CONCLUSION

As for your actual question, the MySQL Query Optimizer would determine the performance metrics of each query when it is done

• counting rows
• selecting keys
• massaging intermittent results sets
• Oh yeah, doing the actual JOIN

You would probably have to coerce the order of execution by rewriting (refactoring) the query

Here is the first Query you gave

select count(*)
from   table1 a
join   table2 b
on     b.key_col=a.key_col
where  b.tag = 'Y';

Try rewriting it to evaluate the WHERE first

select count(*)
from   table1 a
join   (select key_col from table2 where tag='Y') b
on     b.key_col=a.key_col;

That would definitely alter the EXPLAIN plan. It could produce better or worse results.

I once answered a question in StackOverflow where I applied this technique. The EXPLAIN was horrendous but the performance was dynamite. It only worked because of having the correct indexes present and the use of LIMIT in a subquery.

As with stock prices, when it comes to Queries and trying to express them, restrictions apply, results may vary, and past performance is not indicative of future results.

The references in the function's WHERE clause are comparing with the identically named columns in its SELECT clause, rather than the argument list. Try changing it as follows (note the addition of ARG_ to the argument names and the predicates in the WHERE clause):

create or replace function        func_get_Open_Days_2
   ( ARG_SUBMITTED_BY_PERSON_ID in number,
  ARG_SUBMISSION_DATE in date,
  ARG_FORM_VERSION_DATE_TIME in timestamp,
  ARG_FORM_ID in number
   )
RETURN number

IS
   n1 number:=0;
   n2 number:=0;

   cursor records is
      SELECT 
        SUBMITTED_BY_PERSON_ID,
        SUBMISSION_DATE,
        FORM_ID,
        FORM_VERSION_DATE_TIME,
        AUDIT_DATE_TIME,
        STATUS_DATE,
        SUBMISSION_STATUS_CODE,
        CREATE_USER_ID
      from form_state_audit_trail t
      where
        t.submitted_by_person_id = ARG_SUBMITTED_BY_PERSON_ID and
        t.form_id = ARG_FORM_ID and
        t.submission_date = ARG_SUBMISSION_DATE and
        t.form_version_date_time = ARG_FORM_VERSION_DATE_TIME and 
        t.submission_status_code NOT IN (3469, 3462);
      order by t.status_date asc;