Not exactly. Reconciliation is a process created in the Congressional Budget Act of 1974 that does affect both the House and the Senate - but, it probably affects the Senate more because it eliminates the filibuster on these very narrowly defined budget-related bills.
The so-called "nuclear option" (a phrase coined by Trent Lott in the first part of the last decade), describes a parliamentary maneuver that dates back to before the 1830s that would abolish, at least temporarily, the filibuster. Such a maneuver could theoretically be used on any kind of bill in the Senate, not just budget bills.
Thanks ODH — it should be noted that there is a difference between reconciliation and Reconciliation, capital R, that refers, as you point out, to budget-related bills.