There are many differences. The main one is in the fact that `\mathrm{xyz}`

behaves like an ordinary letter, while `\operatorname{xyz}`

behaves like function names such as `\sin`

. Here's an illustration

```
$\sin x + \sin(x+y) + a\sin z$
$\mathrm{sin} x + \mathrm{sin}(x+y) + a\mathrm{sin}z$
```

where it's clear that the second line is typeset wrong. Even if your "operator" requires parentheses after it, it should be `\operatorname`

, as the third summand shows, where a thin space separates the coefficient from the operator.

Another subtle difference is in how some characters are interpreted in `\mathrm`

and in `\operatorname`

. Suppose you have an operator to be called "pre-norm", with a hyphen. Here's the example

```
$\operatorname{pre-norm}(\mathbf{v})$
$\mathrm{pre-norm}(\mathbf{v})$
```

and now it's clear what is to be used. Indeed `\operatorname`

(and the same holds for macros defined with `\DeclareMathOperator`

) treats punctuation symbols in a special way; `\mathrm`

, instead, treats them as math symbols.

Your first version is essentially a *single* equation (that contains several lines of aligned equations, but that is secondary). Your second version consists of *several* equations. This alters the spacing above and below that:

```
\documentclass{article}
\usepackage{amsmath}
\parindent=0pt\relax
\begin{document}
The following calculation is a trivial example
\hrule
\[
\begin{aligned}
q &=CV \\
&=3e-20x1000 \\
&=3e-17
\end{aligned}
\]
\hrule
\bigskip
\hrule
\begin{align*}
q &=CV \\
&=3e-20x1000 \\
&=3e-17
\end{align*}
\hrule
\end{document}
```

yields:

Usually you want the larger spacing around a block of several equations. Your second version is also conceptually clearer.

## Best Answer

The following is taken directly from the

`amsmath`

documentation (section4.3 Dots, p 11):How is it "possible for your document to be adapted to different conventions on the fly"? Well, if you exercise consistent macro usage across the various document elements, a "house tradition" different from the current definition could be employed by using a redefinition. See, for example, the suggestion contained within Consistent typography.

At face value, and purely for comparison reasons, here's a take on

`x,\dots*,y`

: