Difference between 必 and 一定
Since you are not asking what is the difference between '必定' and '一定' or the difference between '必' and '定', I would just go ahead and state the  difference between '必'  and '一定'
From my answer to this question:

Meaning of 的 and 之 when both are used in the same sentence
之 is the classical Chinese counterpart of 的 in modern Chinese

必 is the classical Chinese counterpart of 一定/必定 in modern Chinese
Examples:

Classical Chinese style: &quot;兵家(必)爭之地&quot;
Modern Chinese: &quot;軍事決策者(一定/ 必定)會去爭奪的地點&quot;

~

Classical Chinese style: &quot;中此毒者(必)死&quot;
Modern Chinese: &quot;中了這個毒的人(一定/必定)會死亡&quot;

~

Classical Chinese style: &quot;日軍稱三月內(必)亡中國&quot;
Modern Chinese: &quot;日本軍方宣稱三個月內(一定/必定)能覆亡中國&quot;

'必' on its own has other meaning and usage, but the question only asked for the comparison between '必' and '一定'. The most obvious difference between the two is as this answer stated.
Notice: Actually, I should say '必' is more literary and '一定' is more colloquial because classical style wording appear mostly in writing