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I have seen debris--not trash--that waves bring to the sea from the coast. These may include coast plants, e.g. small pieces of broken branches of trees, grass, bamboos, etc. These can travel miles away from the coast, floating on the surface. This is different from driftwood that waves bring back to the shore!

In the past, it was a sign let sailors know they were close to shore, just several miles away.

I tried to find a word that best describe this in English. Is there any word or phrase?

Ancient floatsam modern flotsam

Flotsam is defined as debris in the water that was not deliberately thrown overboard, traditionally as a result from a shipwreck or accident. As such it belongs to the former owner who can reclaim it.

We usually combine it with jetsam which is discarded rubbish, normally thrown overboard. Which becomes the property of the finder.

Collectively they are used for floating "Marine debris" which is defined as any persistent solid material that is manufactured or processed and directly or indirectly, intentionally or unintentionally, disposed of or abandoned into the marine environment or the Great Lakes. The Government of Japan estimated that the 2011 tsunami created 5 million tons of marine debris.

When found on the beach marine debris can be called tidewrack.

So floating on the sea it is best described as simply wrack which includes marine vegetable matter such as "Bladder Wrack" seaweed.

[Interesting asides] The method by which tree seeds and live animals are carried adrift from land mass to land mass is called "Oceanic dispersal" and can include large rafts of vegetation with living materials e.g. Lemurs to Madagascar. Different to freshwater flotant marshland a floating living island is called a "floaton". A group of similar vegetation (plants or shrubs) is classified as a Free-floating Forb.

The word you're looking for is driftwood:

Driftwood is wood that has been washed onto a shore or beach of a sea, lake, or river by the action of winds, tides or waves. It is a form of marine debris or tidewrack.

In some waterfront areas, driftwood is a major nuisance. However, the driftwood provides shelter and food for birds, fish and other aquatic species as it floats in the ocean.
_Wikipedia

Driftwood is used no matter the size or even if it's just floating in the ocean and hasn't washed up yet. If you need more clarification that it's not large driftwood, you can say something like "driftwood twigs" or "driftwood pieces".

See for example these pages:

• Etsy: driftwood twigs/sticks, driftwood pieces, driftwood necklaces
  


• Alibaba: driftwood chips
  

detritus TFD

1. rock in small particles or other material worn or broken away from a mass, as by the action of water or glacial ice.


2. any disintegrated material; debris.

And from the OED

a. transf. and fig. Waste or disintegrated material of any kind;
debris. b. An accumulation of debris of any sort.

Flotsam, i agree is a good answer! Thus my answer as in generic detritus! I have heard seashore/beach litter also used.

From one google book: Dearie: The Remarkable Life of Julia Child

Rachel and Julia began making funny hats for each other out of
seashore detritus, such as seaweed and lobster claws.

Other possible words which would describe would be:
Floatsam (debris after a shipwreck) or Jetsam (debris thrown overboard from a ship)