Two different things
Hard anodizing is how the body is made: the aluminum is treated in an acid bath with an electric current, which grows a thick, hard oxide layer on the metal. Nonstick is the coating on the cooking surface. Most hard-anodized pans in stores are both. All-Clad's HA1, for one, is a hard-anodized aluminum body with a PTFE nonstick coating and a stainless steel base.
What the hard-anodized body adds
The anodized outside is hard and resists scratches, and All-Clad says its steel base adds durability and resistance to warping. Made In advises choosing a hard-anodized or stainless body over plain aluminum for a coated pan, because plain aluminum warps more easily. The coating inside is still what wears out, on either kind of body.
Stove, oven and dishwasher
Aluminum isn't magnetic, so a hard-anodized pan works on induction only with a steel base. HA1 has one, though All-Clad excludes its HA1 griddles, grill pan and roaster. Oven limits come from the coating and the lids: HA1 pans go to 500°F and their glass lids to 350°F. All-Clad allows the dishwasher for HA1 but suggests washing by hand with a sponge to keep the nonstick working; other makers differ, so check the page for your pan.
Which one to choose
Read past the label. For a nonstick pan, check the body (hard-anodized or stainless rather than thin aluminum), the stove it works on, the oven limit for the pan and the lid, and the care the maker asks for.
How these comparisons are made
Questions about this choice
Is hard-anodized cookware nonstick?
Usually, but not because of the anodizing. The release comes from the coating inside, and the product page names it: PTFE nonstick or ceramic.
Does hard-anodized cookware work on induction?
Only if it has a magnetic steel base, like All-Clad's HA1. A hard-anodized pan without one won't heat on induction.