According to the dictionary, an equation is "a statement that the values of two mathematical expressions are equal."
More specifically, can the word "equation" properly denote a particular formulation of two equal expressions, the more abstract notion represented by that formulation and all equivalent ones, or both? For example, when asked to "place the equation x = .5y in slope-intercept form," are "x = .5y" and "y = 2x" really two forms of the same abstract notion of an equation, are they two different equations that merely share their solutions, or is "equation" defined in both ways?
The word "statement" in the definition might seem to indicate a requirement of being formulated in a particular way, but I'm suspicious that this would press the definition for more technical precision than was intended. If "equation" does turn out to be more or less synonymous with "equation form," what word can be used to describe the more abstract notion that mathematically equivalent equation forms are meant to reflect?