Hi Grants Mom and Welcome to the DIS!
Disney tickets can be very confusing but I'll try to explain the various admission media to you as best I can.
There are two types of admission media: the Magic Your Way pass and the Annual Pass.
Magic Your Way Passes
The MYW pass can be purchased in any length varying from 1 to 10 days. Each "day" allows you to enter one of the 4 major parks.
For $35 more, you can add a "park hopping" option to the MYW base ticket. This "park hopping" option allows you to leave one of the 4 theme parks and enter another on the same day.
You may also add a "magic plus pack" to any ticket for $45. This "magic plus pack" gives you additional admission to several minor attractions. They include: Disney Quest, Typhoon Lagoon, Blizzard Beach, Disney's Wide World of Sports and Pleasure Island. You may use a "plus' feature on the same day that you visit a park or on a day when you do nothing else. Visiting a "plus" attraction will deduct one "plus" from your ticket but no park days. The number of "pluses" that you receive will depend on the number of days that are on your ticket. A 1-,2- or 3-day MYW Plus ticket has 2 pluses. A 4- or 5-day ticket will have 3 pluses, a 6-day ticket has 4 pluses and 7-, 8-, 9- or 10-day tickets have 5 pluses.
All tickets expire 14 days after their first day of use (giving you a total of 15 days to use them), UNLESS you add a non-expiration feature to your pass. The cost of adding the no-expiration option varies with the number of days on the ticket. A 2-day ticket with no expiration costs an additional $10. A 10-day ticket with no expiration costs an additional $100.
In general, it is cheaper to buy any ticket of 4 days in length or more online from a ticket broker.
Annual Pass
An AP is good for 365 consecutive days of admission to all 4 major WDW parks. They cost $420.68/$357.84 (adult/child) and can only be purchased from Disney. The AP promises you to admission to the park and nothing more. However, AP benefits and special offers occur on a regular basis. These benefits can include food, room and shopping discounts. Free parking in the parking lots at the parks is another benefit. Passholders are often invited to special preview events (like the opening of Soaring this month). There are also special passholder-exclusive pins.
A Premium Annual Pass allows 365 consecutive days of admission to all 4 major parks plus the waterparks, Pleasure Island, WWoS and DQ. The cost is $548.49/$466.49 (adult/child) and has the same benefits as the AP.
For the most part, APs are a good idea if you are going for more than 13 days or if you will make multiple visits within a year's time. The discounts alone may not make it worth purchasing one. The room discounts are not guaranteed to be available for your selected dates or resort.