When you use the Share option on a different app, you will likely see Pulse SMS as one of the apps where you can share the content.
Pulse SMS has two options/targets. Using the "Pulse SMS" target will open up the same compose screen that you usually see when composing a message from within the app.
The Quick Share target, on the other hand, opens a smaller pop-up dialog on top of the current app. This allows you to stay within the current app while sending a text/message.
You can use whichever you like and they have the same functionality.