begin{doublespacing} Versus begin{spacing}{2.0}

With a 10pt (default) font size, the setspace package sets the following stretch factors for onehalfspacing and doublespacing: 1.25 and 1.667. I guess the rationale for this is that for many common fonts -- including Computer Modern and Times Roman -- the baselinestretch is 1.2 times the nominal font size. Sure enough, 1.25 * 1.2=1.5 -- 50% more than the nominal font size -- and 1.667 * 1.2=2.0 = twice the nominal font size.

If, in contrast, you run begin{spacing}{2.0} or, equivalently, setstretch{2.0}, you get even wider spacing -- by a factor of 1.2 -- than "doublespacing".

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Addendum to address the OP's follow-up comment: I'm not sure I understand the comment completely, but I believe it asserts that using the spacing environment (provided by the setspace package) with a factor of 1.667 produces line spacing that's different from using the command setstretch{1.667}.

Please consider the following test program, which twice typesets a paragraph of filler text (produced via lipsum[3]) in a two-column document. The left-hand column uses the environment begin{spacing}{1.667} ... end{spacing}, whereas the right-hand column uses the command setstretch{1.667}. Sure enough, the line spacing in both paragraphs is the same.

The outcome is the same if one (a) replaces begin{spacing}{1.667} with doublespacing and (b) omits the instruction end{spacing}.

documentclass{article} 
usepackage{setspace,multicol,lipsum} 
begin{document} 
begin{multicols}{2} 

% Left-hand column:
begin{spacing}{1.667} 
lipsum[3] 
end{spacing} 

% Right-hand column:
setstretch{1.667} 
lipsum[3] 

end{multicols} 
end{document}