I think the way you classify things can confuse you. Voice and unvoiced are two types of sounds in a certain category. Flat sounds can be either voiced or unvoiced; this is not the third type of sound in the same category.
As for your initial question, I would not consider the plus and transition sounds equivalent. Flat sounds - this is when you temporarily block the air outlet, and then release it all at once - think about creating the sound "b" or "p". Transitional sounds are like clicks, pops or bangs. Short, impulsive sound. The positives can be similar, but they can also be longer in duration.
One more thing about vocal cords. I think the terminology gives the wrong image. You do not have cords or strings in your throat that are tense or relaxed. You have two folds that can combine or stay open. A deep sound is when the folds are relaxed and isolated. Voiced sound is when folds beat against each other at regular intervals many times per second.
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