Can somebody please tell what is the difference between these two date comparisons?

You shouldn't use either of these forms. This - 3 shorthand is a timebomb waiting to happen (see this post and this video), and converting to a string and back is one of the least efficient ways to strip the time from a datetime type (see this post).

If the column is date, you should explicitly subtract 3 days from today at midnight, which can be obtained by simply converting "now" to a date type:

WHERE f.DATE >= DATEADD(DAY, -3, CONVERT(date, GETDATE()));

As an aside, you also should avoid using reserved words (like DATE) as column names.

The SQL Server GETDATE() function returns the exact date and time as it at the time of execution including the seconds/milisecond i.e. 2020-07-24 14:08:40.670. When the query executes, the

GETDATE()-3

evaluates the date/time as it at at the time of execution minus 3 days i.e. 2020-07-21 14:08:40.670 and thus only items with an f.Date greater then/equal to 2020-07-21 14:08:40.670 will be returned.

Using CONVERT with a Style of 101 on GETDATE() returns a date in the format of mm/dd/yyyy. In your example above of

CAST(CONVERT(VARCHAR(10),GETDATE() - 3,101) AS DATETIME)

the

CONVERT(VARCHAR(10),GETDATE() - 3,101)

evaluates the date/time as it at at the time of execution minus 3 days without any time portion i.e. 2020-07-21. When this is then CAST to a datetime the time portion is defaulted to 00:00:00 i.e. 2020-07-21 00:00:00.000.

As the derived expression in your second statement is earlier than that in the first you may have additional rows returned.