Each passage expresses concern for the ritual (not physical) cleanliness of a vessel. While none deals with “inner” versus “outer” attributes, problems of ritual cleanliness could occur as liquids are poured from one vessel to another. A controversy current during Christ’s time was whether a liquid poured from a clean vessel into an unclean vessel made the clean vessel unclean. At issue was the liquid’s ability to conduct “uncleanness,” somehow traveling upstream through the liquid connecting to two vessels. Differing resolutions of this question came from the community of the Dead Sea Scrolls and from the Pharisees.
Moroni’s metaphor indicates a question about how to restore cleanness to a vessel. He cites a rule of washing the inside, then the outside, probably assuming that the contents of the vessel had created its uncleanness and that the interior had to be purified first so as not to contaminate the outside with some of the unclean liquid. Of course, we cannot be certain that this is the meaning, but in this context Moroni’s reference makes the greatest sense.