The verb d-b-r (דבר) is to speak—i.e. it is more formal and intentional. Hence words put in writing are also dbrim* (‘dvarim’); the Ten Commandments in Hebrew are Aseret Hadibrot (The Ten Proclamations); and religious prophets always warned civic leaders to honour at hdbrim awr H’ xivh* etc. (the things that the Lord commanded).
The verb a-m-r (אמר) refers to any spoken word. In the narrative-past form common in the Hebrew Bible, it appears most commonly in the form viamr (ויאמר, pron. vayomer = ‘and he said’). Thus, when Adonijah visits Bathsheba (I Kings 2:15), he says:
viamr, at idyt ci-li hiith hmluch, vylii wmu cl-iwral pnihm lmloç; vtisob hmluch vthi laki, ci mihvh hiith lo.*
(‘And he said: As you know, the kingdom was mine. All Israel looked to me as their king. But things changed, and the kingdom has gone to my brother; for it has come to him from the Lord.’).
The difference between the two words is beautifully illustrated in Bathsheba’s reply:
vyth, walh akt anoci woal maitç–al-twibi at-pnii; vtamr aliv, dbr.*
‘And now, I have one request to make of you. Do not refuse me; and she said to him: Speak.
*Shown here in SimHebrew, to maintain the d-b-r root of the Hebrew, which is lost in phonetic rendition (dvarim)