I checked out this link, and it says: "Macros can be aggressive towards each other and other species of shrimp and fish. Many are predatory or opportunistic and will maim or eat dwarf shrimp if they get a hold of them."
Exactly...when you are talking about freshwater shrimp, there are essentially 3 main "groups" you could be talking about.
Most common are what are known as the "dwarf shrimp." These typically grow to only about 1.5" or so at full adult size, and are extremely peaceful to themselves and anything else in the tank. This group would include most of the decorative shrimp in the hobby: ghost, amano, red cherry, yellow, crystal red, tiger, bee, and a host of other shrimps. These shrimp are typically scavengers & omnivores, mostly eating algae and other microfauna (bacteria, fungi, etc.) growing on your tank substrate, plants, driftwood, and so forth.
The second main group are the macros. These shrimp can often be much, much larger (3-4" in body alone, some with a large claw that can add another 2-3" to their total length), and while also scavengers, tend to be much more aggressive--both amongst themselves and towards anything else in a tank with them. One macro of any decent size in a tank of dwarf shrimp can easily wipe out the dwarf shrimp population in short order. These guys are hunters. The most commonly seen ones are the fuzzy claw, red claw, and rusty macros.
The third main group are the "filter feeders." Unlike the other two groups, these guys have large, fan-shaped appendages and feed by filtering microscopic foods out of the water column. Thus they need tanks with significant current and lots of "stuff" in the water column in order to survive. The most commonly seen shrimp in this category is the bamboo shrimp (also called the wood shrimp).
Best place to start learning about these that I know of is Petshrimp. Read through the articles there, especially the ones called "How to Keep Dwarf Shrimp -- An Introduction" and "Beginner's FAQ".