Latex: align vs. aligned vs. eqnarray

align vs. aligned

These three environments are different. First, align and aligned requires amsmath package, but eqnarray does not require any additional package. Let's start talking about differences between align and aligned first. Then, move to differences between alignxx and eqnarray. align is full math environment and self dependent. align does not need to be inside \[ and \] or something else such as gather. Within align, each line will be counted as a different equation; namely, equation number is counted for each line. 

Notice that, within gather and aligned, a whole bunch of equations is counted as a single one. So
what if aligned is in align? In this case, all equations will be counted as one, since aligned is the
most local usage. A result looks exactly the same as using gather in this case.

alignxx vs. eqnarray

Now, let's talk about the differences of usage between alignxx and eqnarray. In eqnarray, parts
between each alignment symbol & are counted independent. For instance, if math equations are
centered, each part will be center on itself. 

Alignment symbol & in eqnarray does not force
elements to be at the same column; it just separate two parts in the same way as separating columns
in table environment. Plus, each line in eqnarray is counted as a new equation. It is important to
emphasize again that alignxx needs amsmath package, while eqnarray does not.