Inner Join On Clause Statement?

I have 2 sql's statement below, and just wondering if their is difference between the two sql's.

FIELDS data type:
--------------------
a.field is DATE
b.field is also a DATE

SQL1:
-------
SELECT a.*, b.*
FROM table a
INNER JOIN table b
ON a.field = b.field
WHERE a.field between b.field AND b.field + 2
;

SQL2:
-------
SELECT a.*, b.*
FROM table a
INNER JOIN table b
ON a.field between b.field AND b.field + 2
;

OR

SELECT a.*, b.*
FROM table a
INNER JOIN table b
ON a.field >= b.field AND
a.field <= (b.field + 2)
;

which ever is correct between the two sql.

QUESTION: would be the two sql's generate same result set.