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Understanding "logical OR" and "logical AND" in programming languages

Many programming languages - most notably Python, but the question applies generally - either have keywords like `or` and `and` used for logic, or equivalent operators such as `||` or `&&` - which are referred to as "logical or" and "logical and" respectively in the language documentation. However, these tools don't seem to work in a natural or expected way for many beginners. Which is to say: "translating" an English sentence into code, using `or` or `||` to represent the English word "or", etc., commonly causes errors or gives the wrong result.
Why is this? What are the semantics of these operators, and how is that different from a natural-language understanding? And why are they called "logical"? (Are there other kinds?)

Many programming languages either have keywords like `or` and `and` used for logic, or equivalent operators such as `||` or `&&` - which are referred to as "logical or" and "logical and" respectively in the language documentation. However, these tools don't seem to work in a natural or expected way for many beginners. Which is to say: "translating" an English sentence into code, using `or` or `||` to represent the English word "or", etc., commonly causes errors or gives the wrong result.
Why is this? What are the semantics of these operators, and how is that different from a natural-language understanding? And why are they called "logical"? (Are there other kinds?)

language-agnostic language-design logic

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