One man’s trash is another’s treasure. But what’s one man’s garbage? Perhaps it’s another man’s compost pile.
What makes the above sign appear nonsensical is the similarity of the two words, often used interchangeably. But what distinguishes them, in actuality, is that trash is commonly considered to be discarded matter generally, while garbage is wasted or spoiled food product. An old, broken child’s toy might be trash; the same child’s uneaten spinach is garbage. One might say that trash doesn’t generally draw flies, but garbage does.
Both words have additional possible meanings.
Trash could refer to any product of poor quality. Sometimes it is used in a derogatory sense in reference to people of low social standing.
Garbage may generally refer to something worthless or meaningless.
Refuse (ref-yoos) is regarded as a synonym for trash, but not garbage.
Sometimes we are asked to separate out different items within our trash: empty cans here, paper products here, glass here, etc. Garbage, on the other hand, seems always to be pretty much just garbage, designated for a garbage can.
Interestingly, my unabridged dictionary distinguishes a dump from a landfill by saying the former is for garbage and the latter for refuse. I suspect that fine distinction breaks down in reality, however.