Same query. different join syntax.
The first is old style ANSI, the latter is later ANSI. If you must pick between them, pick the latter.
I wouldn't use either of them due to the limitations of USING (can't be aliased). Instead write as:
UPDATE table1 A
INNER JOIN (SELECT id,COUNT(*) idcount FROM table2 GROUP BY id)
ON B.id = A.id
SET A.Freq = B.idcount
See this Oracle answer as to why
USING is not to be preferred: http://stackoverflow.com/questions/456684/mixing-using-and-on-in-oracle-ansi-join
And here is a similar discussion for SQL Server: http://stackoverflow.com/questions/1599050/ansi-vs-non-ansi-sql-join-syntax
In general, get used to writing SQL syntax in a way that is portable. While you may never port your code, you will at least be able to port your skills around to multiple database (Which is generally a cool thing to do to avoid becoming a one-trick pony).