Differences between // and /descendant in XPath selecting multiple children

According to XPath 1.0, §2.5 Abbreviated Syntax:

// is short for /descendant-or-self::node()/

So div[@class='popupContent']//input[1] (same as div[@class='popupContent']/descendant-or-self::node()/child::input[1]) will:

1. go to all descendants (children, children of children and so on) of the divs with that "popupContent" class,
2. then look for <input> children
3. and finally select the first child of its parent ([1] predicate)

div[@class='popupContent']//input[2] is very similar except the last thing is to select the 2nd child. And none of the <input>s are 2nd child of their parent.

div[@class='popupContent']/descendant::input[2] on the other hand will:

1. go to all descendants of the divs with that class,
2. selecting only <input> elements, and build a node-set out of them
3. finally select the 2nd element in that node-set, in document order

You can read about predicates and axes in §2.4 Predicates. Relevant pieces:

(...) the ancestor, ancestor-or-self, preceding, and preceding-sibling axes are reverse axes; all other axes are forward axes.

[Thus descendant is a forward axis.]

The proximity position of a member of a node-set with respect to an axis is defined to be the position of the node in the node-set ordered in document order if the axis is a forward axis (...). The first position is 1.

A predicate filters a node-set with respect to an axis to produce a new node-set. For each node in the node-set to be filtered, the PredicateExpr is evaluated with that node as the context node, with the number of nodes in the node-set as the context size, and with the proximity position of the node in the node-set with respect to the axis as the context position;

The only difference between //X and /descendant::X is when X contains a positional predicate, for example //x[1] vs /descendant::x[1]. In this situation //x[1] selects every x element that is the first x child of its parent element, whereas /descendant::x[1] selects the first descendant x overall. You can work this out by remembering that //x[1] is short for /descendant-or-self::node()/child::x[1]