Do the two words mean the same thing?
1. underline = a line directly under letters,
words, etc.?
2. underscore = a line underneath between
letters? between___words
Thank you.
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Comments  (Page 3) 
Having done a great deal of hand typesetting in my youth, perhaps I can help. Underlining was done with a type-high rule extending across a whole line (column) of type, for instance at the end of a paragraph or chapter. Underscoring required a special font of type that had the underline cast on the block of type itself and so became part of the character. (That is why the word underscore is used as a synonym for emphasis, and underline is not.) "Descender" characters often did not have the underscore incorporated in their characters. So, in today's parlance, you could say anything less than a column width line is underscored. If you are attaching the attribute to a paragraph style, it's an underline, if to a character, an underscore. But today, in most people's minds, there's no difference.
An underline is used to underscore an idea for exceptional emphasis from everything else on the page or screen as if saying nothing is more important than THIS. Its effect is lost through overuse. Consider: Quality is job number one. Quality! is job number one. Quality—is job number one. Quality is job number one. The underlined text is attention getting even after you read the text that follows down the page. Even if you are just flipping pages.

For something you are emotionally expressing, you may choose to double-underline it. A lecturer may use a magic marker to double underline an idea of particular importance for the audience to understand and/or follow. In a spreadsheet the TOTAL is often indicated with a double line above the number. Signatures are underlined to underscore their importance.
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