I lived in Hawaii for 6.5 years and first studied belly dance on O'ahu.
Because of those juxtapositions, many people in my area think that I teach hula or can perform it due to a confusion between hula and belly dance.
While I can do some basic hula, it is because I have studied the dance, not because hula and belly dance are related.
The two are similar in a few ways.
Both use bent knees and hip movements.
Both focus on grace, beautiful hands, and subtleties of facial and eye expression.
Hula, though, is essentially a story-telling dance with use of sign and movement to communicate the stories of the gods, chiefs, or the land.
The movements are deep and grounded yet lovely.
(Side note: I would love to spend five years studying sign-related dances: hula, Bharatanatyam [an Indian dance], and ASL dance.)
On the other hand, belly dance interprets the music--it is the embodiment of rhythm, melody, and mood. In pre-Islamic times, dance* would have been used in worship of various gods (and Sufis still use dance as a part of religious ecstasy), but in the present, Middle Eastern dance is primarily used as a dance among women, communal dance, or performance.
There are exceptions, but those go beyond the scope of this incredibly surface level look at the two dances.
What do you notice about the two dance forms? I encourage you to watch Merrie Monarch videos and a variety of belly dance videos to see the differences within hula forms and Middle Eastern dance.
*I don't refer to belly dance but to whatever dance was used at that time.