and will try to respond with as much as I can...
A 1/2 inch sensor can be significantly different from a 1/3 inch sensor. It depends how well each was designed to work with the lens, aperture and "shutter". I've learned that is is all about tradeoffs - a large sensor can work well if the pixel count on the sensor is sufficient, the lens diameter allows enough light in for it to do its job... along with the opening size of the aperture (f-stop), the speed of the shutter and frame rate. Everything needs to work together. Good, large, imaging chips - silicon - are expensive to make. In the 1/2-1/3 inch size, the prosumer and above camcorders are the norm. The good pro camcorders have 2/3 inch imaging sensors... in a 3-chip array.
With a single imaging chip (sensor), the single chip takes care of all three primary colors (Red, Green, Blue - RGB). In a 3CCD or 3CMOS imaging chip array, each chip handles one of the primary colors.
In my opinion: A "cinema camera" is sort of a hybrid between a dSLR and a camcorder. A dSLR is designed to capture digital still images. The decent ones have a single large (APS-C or full frame) imaging chip. These are much larger than most camcorders. A dSLR has an interchangeable lens system - most camcorders rely on a fixed lens (though the better camcorder can add lenses. There are some technical limitations to a dSLR capturing video - for instance, many can overheat during prolonged video capture, there's not much room on the body for useful manual controls (audio gain, zebra, etc.) and they are buried in a menu. And there is a non-technical issue that causes them to automatically stop recording vide at 29 minutes and 30 seconds.
A "cinema cam" is built to be a camcorder, so the file record length is not artificially limited, has the large imaging chip, interchangeable lens system and many times has lots of manual controls on the outside of the camcorder so you don't need to go digging in the menu.
Depth of field is possible through a combination of items working together... again... The long focal length of the lens used helps a LOT. Having a large imaging chip also helps because of the way the aperture and shutter (with the lens and imaging chip) let light in to the imaging chip.
I don't quite understand what is meant by a "good camera compromise". The above missive about dSLRs does not mean they cannot capture good video - they can, and many use them for that purpose. But they do have limitations that have workaround requirements not necessarily geared to a novice.
Generally "pixel count" is a measurement used for digital still image resolution. Video resolution has historically been measured using horizontal line count. For video resolution, 480 is standard definition, 720 and 1080 is high definition... and anything above this is "ultra high definition" (now commonly called "4k"). If you look at the rest of the numbers associated with video resolution (the second number is the horizontal row count; first number is column count):
640 x 480 = 307200 (or 1/3 of a megapixel)
854 x 480 = 409920 (or a little over 1/3 of a megapixel)
1280 x 720 = 921600 (or almost a megapixel)
1440 x 1080 = 1555200 (or 1.5 megapixels)
1920 x 1080 = 2073600 (or 2 megapixels)
3840 x 2160 = "4k" resolution
Lens diameter is important if good low light video is required - but the large lens diameter is not the only thing - it must work with a LARGE imaging chip. In my opinion, "pro grade" starts at about 67mm... Larger is better.
What about "aperture control"? The aperture is the camera's iris. It controls the amount of light that comes in through the lens and hits the imaging sensor and provide for depth of field control.
Frankly, if you have to ask these questions, you may be a little in over your head. I do not want to discourage you, but between being a newbie and technically intimidated, this will be exciting times. And we don't know if your budget includes a good tripod or other steadying gear (never shoot handheld), lighting (camera mounted or on stands), mics (there is no single "best" mic - I have 5 different mics in my kit: 2 shotgun, 1 stereo, 1 handheld dynamic, 2 wireless lavalieres), cables, power supplies and high capacity rechargeable batteries from the camcorder manufacturer, cases... a fairly high end computer for editing and an investment in a decent video editor (and learning how to use it). And there's lots more in the way of accessories: headphones for monitoring audio, larger monitor to see better than using the little LCD screen or through the viewfinder, etc... I've been doing this over about 15 years and learn new stuff every time I shoot or edit.
I don't know what sort of "documentaries" you plan. One way is to press record, get EVER|YTHING, have hours and hours and hours of video to review and edit and maybe end up with about 5 minutes of good stuff. Another way is to write up the documentary script and create a shot list to match your storyboard and ensure you get all the shots on the shot list. I've found using multiple cameras (one wide shot, the other close-ups and medium shots - perhaps form a different angle) can make the editing along and keep it interesting. A shot does not stay on the subject much longer than about 4-5 seconds (occasionally a little longer, but not much and not too often). You can do the math on how many cuts that means in a 4 minute "mini-documentary"...
For what it is worth: My current "main" camcorders are a Sony HDR-FX1 and NEX-EA50UH. I occasionally use a HDR-HC1 - and recently added a HDR-AX30V to the mix. I have a couple of Davis & Sanford Pro Vista tripods with fluid heads and a Steadycam Merlin 2 vest system with counterbalanced, articulating arm. Shure SM58 dynamic handheld mic; Audio Technica AT-875R short shotgun mic; a couple of Sennheiser G3 wireless lavs, Audio Technica AT-822 stereo mic and a long barrel Audio Technica AT8004L ENG mic. I do all my editing on Macintoshes using Final Cut Pro X and a few other supporting apps. All this stuff has taken years to collect and learn - and there's more than this (my spouse thinks I'm nuts, but it was either this or golf for a hobby).
If I missed something or if I was unclear, let me know - and I welcome anyone else out there to please chip in and correct/augment this.
I'm getting a camera to begin making mini documentaries, but technology has always been very intimidating to me. So I have been doing the research and these are the things I can't quite figure out.
Is a 1/2 sensor significantly better than a 1/3 censor
The 3 chipsets often advertised, are those the same as the light sensor?
What makes a cinema camera different from a camcorder?
Is a cinema camera just a nice camcorder that has interchangeable lenses?
Is a camcorder defined by the fact it has a variable focal length lens instead of interchangeable ones?
Do cinema camera usually have bigger sensors or full frame sensors?
Is a large sensor what gives you the ability to create a shallower depth of field?
What is a good camera compromise?
Effective Pixel Count
Size of Censor
Lens diameter
Aperture control
Number of chips
Finally, any suggestions for a camera? 3-4k range if necessary though I'd be happier spending 2-3k, if all I am losing are bells and whistles.
Any other details I really need to pay attention to in choosing the right camera?

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