This is a 9V battery pack with on/off switch and a pre-attached 5.5mm/2.1mm center-positive barrel plug. Use this to battery-power your Arduino (or other electronic projects) - it's ready to go out of the box!
Adafruit NeoPixel Digital RGB LED strips come to us in 4 or 5 meter reels with a 2 or 3-pin JST SM connector on each end and separated power/ground wires as shown in the pic below. If you order a full 4 or 5 meters, you get the full reel with both connectors installed (like the pic below).
If you buy less than a full reel, you'll get a single strip, but it will be a cut piece from a reel which may or may not have a connector on it. If the piece comes from the end of the reel, the connector may be on the output end of the strip!