This particular issue is different for Sunni Muslims and Shiite Muslims.
According to most Shia Muslims:
The only Halal seafood or seafood that is allowed to be eaten by Muslims are:
1- Fish that have scales such as Cod, Tuna, Solomon, etc..
2- Shrimps are halal
(Source: Islamic Laws, Grand Ayatullah Sayed Ali Al-Hussaini Al-Sistani)
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According to most Sunni Muslims:
All kinds of fish and sea food; including shellfish; is halah (allowed) to eat (unless it is poisonous). Only Jews and Shiites forbid eating some kinds of sea food.
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All of the time. Shellfish is not kosher, so they would not eat shellfish at all times.
Judaism is the only religion that bans shellfish but does not ban all seafood or all animal-based foods.
Jews, according to the laws or Kashrut, are only allowed to eat fish if it has fins and scales and is not a bottom-feeder. Shellfish does not meet those requirements.
Jews cannot eat shellfish because the Torah forbids it for Jews (Deuteronomy ch.14). They don't have the characteristics of a kosher species. Any living organism that lives in the sea needs to have fins and scales to be Kosher.