About a proverb students have on their diaries

Question

The students I have keep a diary. The two sentences below are written on those diaries.

小さな積み重ねが、大きな差となる

Small stacking makes big difference.

That English sounds awkward to me. It is absolutely google translated and copy/pasted. But since my Japanese and knowledge of their proverbs(if that sentence is one) is limited, I was wondering if the below proverbs would mean what they meant with the Japanese sentence.

Many a little makes a mickle.

A journey of a thousand miles begins with one single step.

Apart from these two, are there any other proverbs that can convey the meaning of that Japanese sentence? Or if I am wrong, what could be the correct proverb? I don't need a direct translation like;

Many small amounts accumulate to make a large amount.

Answer 1

「小{ちい}さな積{つ}み重{かさ}ねが、大{おお}きな差{さ}となる」

is definitely not a proverb.

It is only a "regular" sentence, which seems to be a rephrasing of the "real" proverb:

「塵{ちり}も積{つ}もれば山となる」

which indeed means:

"Many a little makes a mickle." or "A journey of a thousand miles begins with one single step."

Other Japanese proverbs with similar meanings would include:

「ローマは一日{いちにち}にして成{な}らず」 ("Rome was not built in a day.")

「千里{せんり}の道{みち}も一歩{いっぽ}から」 ("A journey of a thousand miles begins with one single step." )

I just used the term "Japanese proverbs" myself, but many of the proverbs used in Japanese actually come from ancient China, Rome, Greece, etc.