The US has no exit immigration, so as soon as you set foot on US soil—and Hawai’i is one of the 50 states thus US soil in the full meaning of the word—you will need to pass through immigration.
Furthermore, the United States require you to go through customs at your first port of entry similar to e.g. Japan or Canada and different from e.g. EU countries (where your final destination handles customs).
Finally, the two legs are not only different flight numbers but also different planes. Taking the data on flightradar24.com for today’s HA446 (Auckland–Honolulu) shows that the plane came from Tokyo Haneda as HA856 before flying to Auckland and will continue as HA16 to San Diego. This is to be expected, considering Honolulu’s Hawaiian Airline’s home base.
For obvious reasons outlined in the first paragraph, the HNL–LAX portion is considered domestic. Thus, after you clear immigration, pick up your bags, clear customs and drop off your bags at Honolulu, you are fully in the US and when you arrive in LAX you will be treated equivalent to somebody who just landed from San Francisco.
It is worth pointing out that if Hawaiian sells you the connection on one ticket, they have already allocated adequate time for you to make your connection and it is their responsibility to get you to LAX if you miss the plane because the connection was to short.