Logical meaning of "within 30 days" compared to "in 30 or fewer days" or "fewer than 30 days"

Within 30 days = You have no more than 30 days. (By itself this does not clarify when the start date or end date is).

Within 30 days of the expiration date = You have a period of 30 days before the expiration date (inclusive).

You must file the form it during the 30-day period immediately before the expiration date = further clarifies that you must file the form inside of that 30 day just before the expiration date (inclusive).

Background

According to Strunk and White (Macmillan, 1979, page 51):

Less. Should not be confused with fewer.

Left-hand column: He had less men than in the previous campaign. [incorrect]

Right-hand column: He had fewer men than in the previous campaign. [correct]

Less refers to quantity, fewer to number. "His troubles are less than mine" means "His troubles are not so great as mine." "His troubles are fewer than mine, means "His troubles are not so numerous as mine."

The OP's Question

From a grammatical standpoint:

• Within 30 days means within any duration of time less than or equal to 30 days (measured from some starting point). The following would all meet the requirement of within 30 days: 1 day, 3.14159265358979... days, 29 days, 29 1/2 days, 29.314159265358979... days.

• Within 30 days or less means exactly the same thing as within 30 days. That is, the "or less"" is superfluous; it doesn't add anything.

• Within 30 or fewer days means within 30 days, within 29 days, within 28 days, ..., within 1 day. It also means exactly the same thing as within 30 days. That is, the "or fewer days is superfluous; it doesn't add anything.

So, it would seem that within 30 days, within 30 days or less, and within 30 days or fewer mean exactly the same thing: within 30 days, i.e., within any duration of time less than or equal to 30 days (measured from some starting point).

If one were to use in rather than within, the "or less" and "or fewer* matter. For example:

• In 30 days means "come back in 30 days" or "submit the form in 30 days", i.e., after 30 days have gone by.

• In 30 days or less means exactly the same thing as within 30 days.

I believe "within 30 days of Dec. 31 mean within 30 after Dec. 31 and 30 day before Dec. 31st

ie anytime between December 1st and January 30th