One implies ordinary income tax while the other is taxed according to capital gains tax, but how would you convince the IRS that your dividend payment is a special one and should be taxed at capital gains tax rate?
Regular dividends are paid on a preset schedule. If a company pays dividends, it's common to pay them every quarter.
Sometimes a company will pay an extra dividend outside this normal schedule, due to a one-time activity that creates a sudden large influx of cash (e.g. a merger or acquisition). This is a special dividend.
I don't think there's any difference in how they're taxed. However, special dividends can affect tax planning -- regular dividends are usually at the same rate, so you can predict what you'll receive for the rest of the year (the Board of Directors declares the dividend periodically, but it's usually a rubber stamp to keep the same rate). Special dividends are unpredictable so you can't easily plan for them. But they're also pretty rare.
Note that this predictability is only for individual stocks. Mutual funds are more variable because composition of the portfolio changes over time. They don't generally pay special dividends; they receive the special dividends from the stocks they own, but they're incorporated into the dividend distributions they pay out on a regular basis.