I suppose a prime example of a Taker would be Fox Talbot who was trying to find a recording medium for the image and a prime example of a Maker would be someone painting a picture with pixels on photoshop, that had no underlying photographic image.
That's what I assumed you meant. But, in photography discussion, the term "make a photograph" also refers to what you're calling "take a photograph". So most of the discussion here has been along those lines. Very few people who use film do much in the way of image manipulation (beyond the straightforward stuff like cropping, dust-removal, contrast adjustment, dodging-and-burning). So that leads people to consider the casual snapshot as taking a photo and the more careful selection of composition, focus, exposure, aperture, lighting - even of a spontaneous scene (like street photography - to be making a photo.
Then there's what Ralph said, which is taking a photo is when you aren't the creator or arranger of what's being photographed and making is when you have control over or have created what you're photographing (like a still-life, models in a studio, etc.).
So we're all talking about different things. As usual.
