In my experience, je veux dire tends toward “mean” and je voudrais dire is used for “I want to say.”

• Permettez-moi vous expliquer ce que je veux dire.
• Je voudrais dire deux choses à propos des pays pauvres.

Of course, they are both vouloir + dire

It is correct.

Usually, the disambiguation is made by the punctuation and/or the context (I used the English notation for French dialogues since I don’t know how to properly do it):

Vous voulez dire quelque chose ? -> Do you want to say something ?

‘Je cherche quelqu’un.’ ‘Vous voulez dire "quelque chose" ?’ -> ‘I am looking for someone.’ ‘You mean "something"?’

Je veux dire merci à tout le monde. -> I want to say thanks to everybody.

‘Merci à Max !’ ‘Et les autres ?’ ‘Je veux dire, merci à tout le monde !’ -> ‘Thanks Max!’ ‘What about the others?’ ‘I mean, thanks to everybody !’