Dan,
Sometimes folks use both fast and soft to mean the same thing. Normally, that really isn't the case.
Lots talk about rods in general.
First you have a power rating. Essentially, this is how strong the rod, is - i.e. how heavy line it will carry, and is the overall strength of the rod. Typically, we find things like light, medium light, medium, medium heavy and heavy. Often you can translate these names to give a feel for the hardness or softness of the tip.
For example, you might call a light action rod one that has a soft tip.
In contrast, you might call a heavy action rod, one that has a hard tip.
Essentially, when you are talking about a hard or soft tip - you are talking about how easy the top 6 inches to foot of the rod bends. i.e. if the very tip of the rod bends easily; you would call it a soft tip. If the very tip of the rod bends hard, you would call it a hard tip.
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Now - lots talk about rod action.
A typical rod would be called slow, moderate, fast, or extra fast.
The rod action refers to what part of the rod bends as the rod loads, or as a load is brought onto the rod when catching a fish.
In a rod which has slow action, nearly all of the rod or at least the top 2/3rds of the rod all tends to bend at the same time. i.e. one would call this rod one that has a nearly perfect arc - starting relatively close to the butt of the rod. A classic examle of such a rod would be a long steel head rod. This type rod is often used to catch large fish on very light line. The long soft slow action allows a lot of the rod to absorb the runs and surges that happen when a big fish like a steel head makes long and or sudden runs.
A moderate action would be a rod that would make a perfect lindy rigging rod. A moderate action rod tends to have most of its bend in the top 1/ of the rod, and is a generally uniform bend. This makes an excellent lindy rigging rod, because a lot of tip movement can be observed, before the rod begans to feel the stiffness of the butt of the rod, as it takes line.
A fast action rod is one which has its initial bend in the upper 1/3 of the rod. Many general purpose rods have this action, because it can be used for many different purposes. It doesn't make a bad jigging rod, or crank bait rod, or even a float rod - although a moderate action rod would be a better choice for a float rod.
Then you may have an extra fast rod. This is one which has its initial bend in the upper 1/4 of the rod. This is the classic walleye jig stick. It is the perfect rod for fishing a jig and minnow combination. The very sensitive ( and sometimes semi soft) tip is the perfect tip for sensing those light bites. The quick taper of the rod, quickly stiffens as the rod progresses toward the butt of the rod. This rod action, then allows for the necessary quick hook set that is essential for excellent hook sets when using a jig to catch fish.
I trust that some of these explanations will help to answer your questions.
Take care
REW