Both the terms 'mood' and 'modality' have been extensively used in the English grammar. First and foremost, modal auxiliaries such as 'can', 'may', 'should', 'must' are said to represent the 'mood', not 'mode', when 'modal' etymologically derives from 'mode', not 'mood'. For example, Oxford Dictionaries has this definition for 'modal':
2 Grammar Of or denoting the mood of a verb.
What's funny is, when you click on the word 'mood' in the dictionary's definition, you're directed to the following definition of 'mood' in the dictionary:
1 Grammar A category or form which indicates whether a verb expresses fact (indicative mood), command (imperative mood), question (interrogative mood), wish (optative mood), or conditionality (subjunctive mood).
This definition doesn't seem to be the right definition of 'mood' used in the definition of 'modal'. And I think that all this confusion arises from the misuse of the word 'mood'.
If I'm mistaken about all this, please someone enlighten me as to any profound reasoning behind the adoption of 'mood' instead of 'mode'.
After reading the answers and comments, I've isolated the cause of my confusion, although no other seems to share this confusion. According to the above definition of 'modal', it denotes the mood of a verb. In today's English, however, the only instances where a verb (without the help of a modal auxiliary) indicates 'mood' are limited to the subjunctive and the imperative mood. For example:
[i] If I were you, I would be careful. [subjunctive mood]
[ii] She suggested that he be careful. [subjunctive mood]
[iii] Be careful. [imperative mood]
John Lawler argues somehow that an English verb (without the help of a modal auxiliary) can indicate all the other types of moods such as the indicative, interrogative, optative. But can it? If anyone thinks it can, please provide an example sentence.
Even in [ii] and [iii], the same form 'be' indicates both the subjunctive and the imperative moods. So technically speaking, there is no such thing as the mood of the verb 'be' per se, unless it's put in context as in [ii] or [iii].