These are different branches on the tree of life, specifically within the plants. If you imagine this tree of life, species would be the tips of the smallest branches. And the branches itself would be different units (=taxa) that lead to various branches. So in taxonomy we use special words for these different units/taxa dependent on how far back they are removed from the species. Like, you may have heard of a genus. For example we as humans are the species Homo sapiens and our genus is the first part of that: Homo. There were also other species in that genus, like the Neanderthals (Homo neanderthalensis) or the Denisovans (Homo denisova). This works the same in plants. For example ginger is actually the species Zingiber officinale. There are also other gingers, like Zingiber spectabile. If we go one level up the branch, we reach the family ginger is in: Zingiberaceae. In this “ginger family” we have other plants of different genera like turmeric (Curcuma longa) or cardamom (Elettaria cardamomum). Notice how the first word of these species isn’t Zingiberales, because they are in other genera. So, Zingiber is more closely related to any other Zingiber than it is to the other plants in Zingiberaceae. And one level above, Zingiber is more closely related to any plant in the Zingiberaceae than to any other plant. Taxonomy is based on who evolved from whom, that’s why it is important what are the closest relatives to a given species.

This is fundamentally what taxonomy is about. From there on we can go up the branches of the tree of life and explore the branches that connect to even more species. If we go up one major level from the family we reach the “order” (I’m simplifying here, taxonomy is much more intricate than that). An order of plants contains various families and the OP spoke of the order Zingiberales (ending in -ales). The “words” I’ve used are families (ending in -aceae) as you might have expected from Zingiberaceae above. And the families I’ve listed in the first half are all within the same order of Zingiberales. These are all very common ornamental or otherwise cultivated plants. You may know Marantaceae as calantheas/goeppertias/prayer plants, Heliconiaceae as lobster-claws. Other important members of this order are also bananas (Musaceae).

In the second half of my comment I talk about Poales and seaweeds not being Spermatophyta. So, Poales as you might have guessed from the ending is a separate order of plants. In it are most prominently the grasses (Poaceae) OP spoke about in their post. And seaweeds not even being Spermatophyta means they aren’t even seed plants.

I hope this explains it :)