The sawmill waterfall was created using a conveyer style texture on a model. The same texture works on brushes as well, and presumably displacements.
You can find out how the texture was programmed to roll by extracted the material file's accompanying .vtf (Valve Text File) from the GCF (Game Cache File) using GCFScape:
http://nemesis.thewavelength.net/index.php?p=26
Which allows you to access and export the encrypted files.
You want to look in
Team Fortress 2 Materials.gcf, in there look in
tf/materials/models/prop_forest for the waterfall model and all its files.
From there you will need to look at the accompanying text file (.vtf extension) which defines the materials properties. Such as the bullet decal to use if it's a solid prop, the ricochet type (wood, spark, concrete etc) and sound it makes when you walk on it etc. This file also defines whether the texture will roll, and at what speed).
The waterfall seems to have two .vmt's. waterfall001.vmt and waterfall001_solid.vmt. Presumably this is because the model has 2 layers that use a solid, and an alpha transparency; to make it look more realistic in game. I imagine they use the same .vtf as there is only one of them.
Unfortunately i can't tell you what the settings are to add to your .vtf file in order to get your texture to scroll but i'm sure someone else can, or you can just google it.
Particles are a different entity all together. They allow you to create small effects that are basically a more sophistaced type of sprite, like the splatting of blood when you shoot someone, splashes on the surface of water, or the flashing light you see ontop of the payload when it's being pushed. Particles are used to create the wake effects and waterfall splashes you see on the water and rocks in sawmill, for example.