What is the difference between accrue, accumulate, and collect?

The words mean pretty much the same thing.

In practice, one or the other tends to be preferred in any given context. Like we say that a person "collects stamps" or "collects classic cars", not that he accumulates them. But we say that a person "accumulated a large sum of money" or "accumulated a pile of trash".

"Accrue" is rarely used except with the specific technical meaning that Dilip refers to: something that is due you but that you haven't yet collected. The only examples I can think of off the top of my head are interest on a deposit, as in, "Interest is accrued daily and paid monthly", and vacation time or sick time, as in, "You accrue one and a half vacation days per month worked." (You don't necessarily have to take off one and a half days every month, but you accumulate the right at that rate.) Occasionally people use it to mean "accumulate" in a more general sense, like, "He accrued experience over the course of many years", but that's pretty rare.

I'm grasping for a general rule of when to use "collect" versus "accumulate". Perhaps "collect" has the connotation of selecting individual items, while "accumulate" is used more for an amorphous quantity. You "collect a debt" but you "accumulate wealth" -- the debt is specific but the wealth is general. You "collect fine china" but you "accumulate dishes". Etc.

These words are all very similar but have different semantics.

Accumulate: Means to increase gradually, either in volume or number. An interesting thing about accumulate is that you can accumulate things, but things themselves can also accumulate. You can accumulate wealth, or stories, or stamps... but water can accumulate in your basement, and dishes accumulate in your sink.

Accrue: Means accumulate, but used primarily in finance and law.

Collect: Means accumulate, but leaning more toward to gather, to bring together into one place.

Accrue is more closely defined as "Earn". You "Accrue rewards points when you charge things on your credit card". You earned those points.

Accumulate is simply increasing count... He accumulated a large quantity of junk and is now a hoarder. Accumulate often implies a passiveness. Something that just happens over time.

Collect implies a more active accumulation, but not always. "Rain collected in the barrel" but also "He collected his earnings for the days shift".

So the answer is that each of these has a subtle primary difference, but in reality can be used interchangeably in many situations.

I agree, "accrue" is less tangible, more conceptual. It means something like "inure." It describes the motion/direction of something you're counting, when adjusting to show what of it has actually been earned or incurred during a given period of time. "Accrued" means something like "counted (toward/against)."

"Accumulate" is more tangible. Simply, where once there was dry pavement, now there is a pile of stuff, which has been gradually piling up, and may continue to pile up even higher (and who cares why it's piling up). "Accumulation" describes the size of the pile at a given moment in time, and implies the pile was smaller in the past and will get bigger in the future. "Accumulated snowfall." This also works in reverse, for example if you're trying to account for how much value your car has lost as of a given date. "Accumulated depreciation."