If you're not in the mood to read below, my quick answer to you is to get an AVerMedia Game Capture HD.
There are plenty of types of recording devices. Black Magic and HD PVR are at the top of the market but they, in my opinion, are the worst. You constantly have to have your computer plugged into them and they are the bulkiest. They record in full HD and allow you to stream but there are better examples I state further. Roxio Game Capture is probably the worst you can get. The price you find it at is exactly what you get. It records in 720P at best and is just as bad as an HD PVR when it comes to recording. The middle, top-of-the-line (in my opinion) capture devices are AVerMedias. I own the AVerMedia Game Capture HD and I love it. You never have to record with a computer program running and it records in FULL HD 1080P. All you need is a small USB thumbdrive or internal hard drive (2.5 inch) and you can record for hours. I own a cheap SanDisk 32 GB USB and I can record for 272 minutes on 1080P. However, since the Game Capture HD won't stream (which isn't a bad thing because streams aren't too popular with newer YouTubers), there's an alternative. AVerMedia makes a game capturer which is a bit more expensive than the Game Capture HD that runs just like a DVR. It's called the Live Gamer HD.
All AVerMedia devices I recommend to you because I own one myself and it's, by far, the best game capture device I've ever had.
Visit their webstie: http://www.avermedia-usa.com/AVerTV/
The best XBOX recirding device is an HD PVR or Capture Card.
a capture card
You will need a video capture device.
Capture card is a device that allows capturing images from video source, therefore it can be used for recording games from XBOX. Hook up an Epiphan's VGA2USB frame grabber to an XBOX video output and to a PC and start recording a game.
You can grab the video off your Xbox 360 if your capture card accepts component or composite signals.
eBay has a large number of new and used video capture cards for your Xbox. Sort your search by lowest price and you should be able to find a good deal.
Evidently you need a device supporting VGA capture and recording with high resolution from the XBOX 360 output. An Epiphan's capture card VGA2USB LR with lossless signal compression seems to be a convenient solution for your needs
yes
sends video from a device to your tv like a dvd player or xbox or ps3 etc
It can record Xbox gameplay. Basically, records whatever you do.
A V Stick is an input device for Xbox 360 video games.
Capture card for the XBOX 360 is a solution that helps you to acquire and record signal from the XBOX video output. A high-performance frame grabber (for example, VGA2USB) compresses and optimizes captured data. An XBOX game is recorded to a PC hooked up to a frame grabber.