I'm going to push back hard on this line. Yes, it's the same word but with different connotations.
The Void is empty. Yes, it allows for movement by atoms, but the important thing is that it's empty. It's the emptiness that allows the unimpeded movement.
Empty beliefs, metaphorically, are devoid of any substance. There's nothing that supports them. They arise not from philosophical understanding but from misunderstanding or disregard of the goal of life.
I'll let Epicurus take it from here...
U116. I summon you to unceasing joy and not to empty and trifling virtues, which destroy your confidence in the fruits of what you have. ἐγὼ δʼ ἐφʼ ἡδονὰς συνεχεῖς παρακαλῶ καὶ οὐκ ἐπʼ ἀρετὰς κενὰς καὶ ματαίας καὶ ταραχώδεις ἐχούσας τῶν καρπῶν ἐλπίδας.
U202. He who follows nature and not groundless opinions is completely self-reliant. With regard to what is enough by nature, everything he owns is a source of wealth; whereas with regard to unlimited desires, even the greatest wealth is poverty. ὁ οὖν τῇ φύσει παρακολουθῶν καὶ μὴ ταῖς κεναῖς δόξαις ἐν πᾶσιν αὐτάρκης· πρὸς γὰρ τὸ τῇ φύσει ἀρκοῦν πᾶσα κτῆσίς ἐστι πλοῦτος, πρὸς δὲ τὰς ἀορίστους ὀρέξεις καὶ ὁ μέγιστος πλοῦτός ἐστι πενία.
U221. A philosopher's words are empty if they do not heal the suffering of mankind. For just as medicine is useless if it does not remove sickness from the body, so philosophy is useless if it does not remove suffering from the soul. κενὸς ἐκείνου φιλοσόφου λόγος, ὑφʼ οὗ μηδὲν πάθος ἀνθρώπου θεραπεύεται· ὥσπερ γὰρ ἰατρικῆς οὐδὲν ὄφελος μὴ τὰς νόσους τῶν σωμάτων ἐκβαλλούσης, οὕτως οὐδὲ φιλοσοφίας, εἰ μὴ τὸ τῆς ψυχῆς ἐκβάλλει πάθος.
U422. We need pleasure when in pain because of its absence; but when we are not experiencing such pain, and are perceiving stably, then there is no need for pleasure. For it is not the needs of nature which, from outside us, create harm, but desire driven by groundless opinions. τότε χρείαν ἔχομεν τῆς ἡδονῆς, ὅταν ἐκ τοῦ μὴ παρεῖναι αὐτὴν ἀλγῶμεν· ὅταν δὲ τοῦτο μὴ πάσχωμεν ἐν αἰσθήσει καθεστῶτες, τότε οὐδεμία χρεία τῆς ἡδονῆς· οὐ γὰρ ἡ τῆς φύσεως ἔνδεια τὴν ἀδικίαν ποιεῖ ἔξωθεν, ἀλλʼ ἡ περὶ τὰς κενὰς δόξας ὄρεξις.
U423. What brings unsurpassed joy is the removal of a great evil; and this is the nature of the good, if you apply your mind rightly and then stand firm and do not stroll about chattering emptily. τὸ γὰρ ποιοῦν ἀνυπέρβλητον γῆθος τὸ πάραυτα πεφυγμένον μέγα κακόν· καὶ αὕτη φύσις ἀγαθοῦ, ἄν τις ὀρθῶς ἐπιβάλῃ. ἔπειτα σταθῇ, καὶ μὴ κενῶς περιπατῇ περὶ θρυλῶν.
U471. It is rare to find a man who is poor with regard to the aims of nature and rich in groundless desires. For a fool is never satisfied with what he has, but instead is distressed about what he doesn't have. Just as those who are feverish through the evil of their sickness are always thirsty and desiring the opposite of what they should, so those whose souls are in a bad condition are always poor in everything and through their greed fall into ever-changing desires. σπάνιόν γε εὑρεῖν ἄνθρωπον <πένητα> πρὸς τὸ τῆς φύσεως τέλος καὶ πλούσιον πρὸς τὰς κενὰς δόξας. οὐδεὶς γὰρ τῶν ἀφρόνων οἷς ἔχει ἀρκεῖται, μᾶλλον δὲ οἷς οὐκ ἔχει ὀδυνᾶται. ὥσπερ οὖν οἱ πυρέττοντες διὰ κακοήθειαν τῆς νόσου ἀεὶ διψῶσι καὶ τῶν ἐναντιωτάτων ἐπιθυμοῦσιν, οὕτω καὶ οἱ τὴν ψυχὴν κακῶς ἔχοντες διακειμένην πένονται πάντων ἀεὶ καὶ εἰς πολυτρόπους ἐπιθυμίας ὑπὸ λαιμαργίας ἐμπίπτουσιν.
U485. Unhappiness is caused by fears, or by endless and empty desires; but he who is able to rein these in creates for himself a blissful understanding. ἢ γὰρ διὰ φόβον τις κακοδαιμονεῖ ἢ διʼ ἀόριστον καὶ κενὴν ἐπιθυμίαν· ἅ τις χαλινῶν δύναται τὸν μακάριον ἑαυτῷ περιποιῆσαι λογισμόν.
U486. Pain does not consist in being deprived of things, but rather in bearing the avoidable distress caused by groundless opinion. οὐκ ἀπορεῖν τούτων πόνος ἐστίν, ἀλλὰ φέρειν μᾶλλον τὸν ἀνόνητον ἐκ τῶν κενῶν δοξῶν πόνον.