The Ace Attorney series are visual novel games; I'd call them a crossover of genres.
They have the presentation of a visual novel (first person perspective, characters look straight out at you, most of game is paging through dialogue), but they also have gameplay elements of traditional adventure games (looking around multiple locations for clues, try every item in the inventory to see what response you get, etc.) - I think in Japan they'd call that an adventure game for being overly interactive, but in the West we'd still call it a visual novel.
I haven't tried the Zero Escape series, but after a quick look at one on Youtube, it does look like that same mix of visual novel with adventure game / puzzle elements?
Adventure games that have elements of visual novels have existed for a long time in Japan even though they were often not translated and sold outside of Japan. Examples of this are the The Portopia Serial Murder Case (from Yuji Horii who wrote the scenario for Chrono Trigger), the Jake Hunter games, etc...
They have the presentation of a visual novel (first person perspective, characters look straight out at you, most of game is paging through dialogue), but they also have gameplay elements of traditional adventure games (looking around multiple locations for clues, try every item in the inventory to see what response you get, etc.) - I think in Japan they'd call that an adventure game for being overly interactive, but in the West we'd still call it a visual novel.
I haven't tried the Zero Escape series, but after a quick look at one on Youtube, it does look like that same mix of visual novel with adventure game / puzzle elements?