Can someone explain what is different about the budget "reconciliation" process?

Reconciliation has nothing to do with votes. By the way, most ALL legislation is passed by simple majority in both the house and senate. It takes a 2/3rd majority in .both to override a presidential veto. It is an unusual case which goes to a 2/3rds vote. Anyway, reconciliation is a balancing act, like you do with your checkbook. It is simply adjusting the assets and liabilities to make it balance. In the case of the government, it is a comparison of incoming revenue compared to outgoing liabilities. If the bottom line is not zero, then the budget is not balanced. If the balance is less than the last time, we have a budget "surplus" which does not mean we have a positive bank balance in the treasury, just that we owe a few dollars less on the national debt. "Surplus" to the government simply means that over a period of time, we have more income from revenue than we had incurred in liabilities, which is also termed "reducing the deficit".