The depth of field(focus) and exposure.
Depth of field in photography is 3-dimensional and is measured from the foreground moving along a horizontal plane towards the background. Maximum depth-of-field means most of the scene is in focus and shallow depth-of-field means the minimum is in focus. Shallow depth-of-field lets you lose the background into a nice blur leaving the foreground in focus - good for portrait photography. In landscape photography you would normally choose the maximum depth-of-field so that distant hills were in focus as well as the middle ground and the foreground - in other words, everything in the field of your vision would be sharply focussed.
Possibly by 'field' you mean a category or type, such as Photojournalism, or Portrait, or Wedding photography. Or maybe you refer to 'depth of field', which is the distance front to back in focus. Sorry to be vague, I have worked in photography for many years, and have never considered the idea of 'field' as such.
Manual or Aperture Priority.
In photography, the acronym DOF refers to Depth of Field. This applies mainly in digital photography, and is how focused the lenses are on one area or place.
Infinite, with a suitable lens. In theory, a pinhole camera (which has no lens at all) will have a nearly infinite depth of field, but at the expense of extremely long exposure time.
The largest aperture which is the smallest number on the aperture ring/dial generally anything between f1.2 - f5.6 dependant on the lens and zoom. On most consumer digital cameras the more you zoom in the higher the smallest aperture becomes. eg. Lens at 35mm, widest aperture (shallowest depth of field) generally about f2.8 Zoom in and the largest aperture will reduce to about f5.6
With a 100mm macro lens, as little as a few millimeters, even when stopped down to F16.
I think your question could be re-phrased as the difference between long exposure photography and deep depth of field photography. A long exposure is where a long exposure time is used, either to record movement over a period of time, for artistic effect, or in order to provide a greater depth of field, (deep focus), achieved by using a smaller 'F' number on the camera, which provides a smaller aperture for the light to pass through. ********* For some, it relates to what is technically known as hyperfocal distance (a point of focus deduced and utilized to maximize depth of field beyond normal). IMHO, "deep focus" is a mis-nomer as you can only focus on one plane within the field of view. Anything in front or behind is not in focus; however, it may be acceptably sharp to the eye. This is depth of field. There is also "depth of focus", which is different, though related. Methinks neither depth of field nor depth of focus should be referred to as deep focus
The f-number is indicative of aperture. The smaller the number, the larger the aperture is, and the more light is let in. The Depth-of-Field is also reduced with a smaller f-number. f/1.7 is a very large aperture, and there will be little depth of field, but lots of brightness.
Depth of field is the depth of the specimen clearly in focus and is greater at lower magnifications.
Generally, you can with all cameras. All you need is a shallow depth of field. You can achieve this by using a low aperture (ex. f/2.8, f/1.8) The lower the f/#, the shallower your depth of field will be.