Is there any difference between the phrase "from day to day", "day by day" and "day after day"?

Question

Is there any difference in meaning betweeb the following sentences.

My health is improving from day to day.

My health is improving day by day.

My health is improving day after day.

If there is no difference, then which one is the most common?

Answer 1

All three are idiomatic expressions that mean different things, and they do not all fit your context.

"Day to day" is used in connection with things that are routine and perhaps happen daily.

Example:
"Exercise is part of my day to day routine".

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"From day to day" can denote contrast between one day and the next. It also suggests variance, not necessarily results that trend in one direction.

Examples:
"My duties vary from day to day"
"There is no discernible change from day to day"

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"Day by day" denotes a gradual change that is perhaps noticeable each day. This is the only one that fits your context.

Example:
"My health is improving day by day."

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"Day after day" denotes repetition and is used in connection with things that happen daily. It is not always negative, but perhaps more so than 'day to day'.

Example:
"Day after day he made the long drive to work".

Answer 2

To my ear, from day to day sounds less consistent—as if each day were not necessarily witnessing an improvement. Expanded rationale below.

The others are analogous to formation, grouping and number-related dative expressions in other languages.

Ex.

The ants go marching three by three.

Here the meaning is that three ants pass at once, then three more and three more.

This is the literal meaning of the construction day by day. One day passes, then another. They are passing one by one.

On one hand from day to day is not necessarily enumerating all days, such that some may be omitted when evaluating the overall trend. Therefore there is a possibility of less consistency in the trend. However on the other hand in the context of dative constructions such as “one by one”, “two by two”, “zu dreien” we can see that this is a way Germanic languages (including English) do enumerate each passing item, grouping them by ones, twos, threes, and so on.

Say we do not take from day to day to be identical to day by day. Then we may possibly interpret the (lack of definiteness/anarthrousness) to mean that the days in question are not necessarily mutually adjacent.

Then we could reconstruct a hypothetical schedule in which there are bad days.

• Monday, good
• Tuesday, bad
• Wednesday, good
• Thursday, good

So the sense is that the general timing is on the order of a day between periods of improvement but without the strict requirement that we could check every 24 hours and find an improvement.

Quoting History of the English Language by O.F. Emerson, section 375., numerals.

Our present English distributives, two by two, three by three, are scarcely a preservation from Old English times since and was used instead of by in such expressions, and the numeral was in the dative-instrumental case, as twam and twam 'two by two.' The older form occurs in the Bible, as two and two, Gen. 7 : 9, in Shakespeare, as in Henry IV, III, 3, 104, and some times in present English.

While not supporting the idea of a direct succession from the dative-instrumental to present x-by-x

1. This clearly establishes the equivalent force of the present English distributive.
2. This connects the distributive to related Germanic dative constructions, as claimed.

To say this is not equivalent to [a] day by [a] day, or one day by one day is absurd.