There is such a thing as a "non-iambic" paddle. It has one common contact and one "dit" and one "dah" contact, just like an iambic paddle. Difference is, they use only a single movable lever (like a common SPDT switch), so you cannot possible send a "dit" and a "dah" at the same time. It's one or the other.
With an iambic paddle, two levers are used to you can "squeeze" the two paddles together and close both the dit and the dah contacts simultaneously. If you do, this sends a string of didahdidahdidahdidahdidahdidahdit...and whether that string starts with a "dit" or with a "dah" depends upon exactly which side contacted first. That control is in your hands, as the operator.
When you use squeeze keying in iambic mode, you can select whether the keyer will send one additional bit of data after you open the last contact, to "self complete" some letters. For example, to send the letter "R" you would simply squeeze the paddles together, making sure the dit side contacts first. As soon as you hear the dah that is the central bit of the letter R, you release the paddles entirely, and the keyer will complete the letter didahdit. You don't actually have to "send" the last "dit," yourself; the keyer will do it for you.
Obviously, this feature only works with some letters, but once you get used to it, it does save time and effort and makes sending high speed code a bit easier.
However, just because you have an iambic paddle does NOT mean you have to use it that way!
You can push the levers back and forth to the left and right, just like a single lever paddle, and use it in non-iambic fashion, just fine. Iambic keying is an "option," for you, if you have a dual lever paddle. If you do NOT have a dual lever paddle (non-iambic paddle), the you don't have this option.
Almost all really good paddles on the market today are iambic and provide this feature/option. If you're homebrewing a paddle, it would be easier to build a non-iambic one (fewer parts).