Difference between "//" and "/" in XPath?

/ vs // in general

Both child (/) and descendant-or-self (//) are axes in XPath.

• / is short for /child::node()/.

  Use / to select a node's immediate children.

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

  Use // to select a node, its children, its grandchildren, and so on recursively.

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/ vs // with preceding-sibling::*

Your specific question asks about the difference between //preceding-sibling::* and /preceding-sibling::*.

Since your data is offsite and complex, let's consider instead this present and simpler XML:

<r>
  <a/>
  <b>
    <c/>
    <d/>
  </b>
</r>

For this XML,

1. /r/preceding-sibling::* selects nothing because r has no preceding siblings.
2. /r//preceding-sibling::* selects the preceding siblings elements of all of the descendant or self nodes of r. That is, a, b, c and d. (Remember, /r//preceding-sibling::* is short for /descendant-or-self::node()/preceding-sibling::*, not /descendant-or-self::*/preceding-sibling::*) Note that even though b and d are predecessor siblings to no elements, they are predecessor siblings to text nodes because the above XML has whitespace after b and d. If all whitespace were removed, then only a and c would be selected.
3. /r/descendant::*/preceding-sibling::* selects the preceding sibling elements of all descendant elements of r. That is, a and c. Note that b and d are not selected because they are not preceding sibling elements to any descendant elements of r -- unlike the previous example, text nodes do not qualify.