Acronyms of Tidal Parameters

HAT is highest astronomical tide. It is the highest high tide that occurs in a tidal epoch of 18.6 years.

MHWPS is mean high water, perigean springs. It occurs every 7 months when lunar perigee coincides with a Full or New Moon.

MHWS is mean high water springs. In most places it occurs every two weeks just after Full or New Moon, but for Canterbury it is different, as explained below.

MHW is mean high water. This is the average high tide height.

MHWAN is mean high water, apogean neaps. It occurs every 7 months when lunar apogee coincides with First or Third Quarter.

MSL is mean sea level. It is the level about which tides fluctuate. It is not constant, but varies from days to centuries according to changing atmospheric pressure, winds, and long-term climate effects (like El Nino/La Nina), as well as sea level rise.

MLWAN is mean low water, apogean neaps. It occurs every 7 months when lunar apogee coincides with First or Third Quarter.

MLWS is mean low water springs. Usually, it occurs every two weeks just after Full or New Moon, but see the comments below for Canterbury.

MLWPS is mean low water, perigean springs. It occurs every 7 months when lunar perigee coincides with a Full or New Moon.

LAT is lowest astronomical tide. It is the lowest low tide that occurs in a tidal epoch of 18.6 years.

Because of the way the tides propagate around New Zealand, there is no discernable spring/neap effect on the tides for most of the east coast.
This is illustrated in the plot below comparing tides at Jackson Bay (west coast, South Island) with Lyttelton.
Nevertheless, MHWS is an important tidal parameter for planners. MHWS is usually defined as:

Lunar semidiurnal tide + Solar semidiurnal tide

and in most places this is a tide that is exceeded by only 12% of high tides.
But for Canterbury it is exceeded by 25% of high tides.
Therefore, ECan uses the following definition for MHWS:

Lunar semidiurnal tide + Lunar elliptic tide

and this is the definition used in the tide forecasting page.