Basic answer: it doesn't matter.

if you look at just about any two psychology textbooks, you'll find different definitions - in fact, sometimes the definition for emotion in one book is the same as the one for feeling in another.

The point is that it's not for the sake of intellectual clarity; it's ONLY value is in clarifying your experience.

So let's see if this helps:

The definitions I gave are actually pretty widespread these days, though not entirely

EMOTIONS: mental interpretation of sensations

FEELINGS

Simple feelings; pleasant, unpleasant, neutral

Deeper feelings: Love, compassion, kindness

So let's take your list and see if the above definitions help get us beyond analysis to direct experience:

Confused: Confusion is a state of mind, not an emotion. Do you feel bad about being confused, frustrated, happy, sad, anxious? Those are emotions.

clueless: also a mental state. Do you feel bad about being clueless, frustrated, , etc

frustrated: This is an emotion.

That was easy.

Ok, let's go on:

inadequate; a mental judgment, not an emotion. Do you feel bad, or frustrated at feeling inadequate? Now, most people who feel inadequate feel bad about it. But I could be auditing a class on advanced calculus never having taken a beginner class. I see that my skills are inadequate. I might feel just fine about it. So "inadequate" doesn't necessarily tell me how I'm feeling.

dumb, - A mental description that I feel stupid about something. Again, usually this is accompanied by an emotion - I feel very bad about this, but the word "dumb" doesn't tell me that - I might feel mad that I didn't learn enough, etc.

idiotic, - same as with "dumb" _ I feel like I did something dumb, or stupid, but WHAT was my emotion? Shame, guilt, sorry, anger?

worthless: this is so commonly associated with feeling depressed it seems obvious, but again - "worthless" is an evaluation.

Now do clarifying these words help? If it's a purely intellectual exercise, no, not at all. If the WORD points you to an EXPERIENCE (which by definition is beyond words) then it helps.

Then it doesn't matter if you're doing CBT, DBT, psychodynamic therapy, somatic therapy or whatever. Your nervous system is not likely to change much unless you bring your attention to your actual, somatic, emotional experience. Clarifying your understanding of thoughts, beliefs, emotions and feelings CAN be VERY helpful if you helps you to FEEL the difference between thoughts, beliefs, emotions and feelings and you start noticing how these affect your experience, your body, your state of mind, etc.