Filter Construction and Terminology

Oil filters are usually constructed pretty much the same, overall. Dirty oil under pressure flows into the outer ring of holes on the baseplate, then pushes past an anti-drainback valve on its way to the filter element (the element is the stucture that holds the "paper" media as the top left header picture shows), the dirty oil is then forced through the media which filters it, through the perforated center tube (above right), and out to the engine through the big, threaded center hole of the baseplate.
Should the media become clogged, or the oil too cold and thick to be forced through the media in proper quantity, a bypass valve is forced open (above right picture - center of the tube) to allow unfiltered oil to get to the engine. This is critical. Some filters do not have these, as it is part of the engine itself. One reason it is important to match the filter to the engine.
The anti-drainback valve is normally just a rubbery disc that allows oil into he filter, but resists the oil from draining back out. This is to help keep oil ready to go in the filter and prevent "dry-starts" after the engine is shut off.

There are some differences in not just the quality and quantity of the filtering media, but the type and strength of the materials that hold it all together. Racing or off-road filters tend to have heavier canisters to resist puncturing by rocks or other debris. Since most filters are fairly well up out of the way of ground debris, and most of us do not race, I don't pay a lot of attention to certain physical characterisics such as this. 

The two main things about construction that seem to matter to many people who are picky about the oil filters they buy, are the material that the anti-drainback valve (ADBV) is made of, and the location of the bypass valve.
Silicon and nitrile are the usual materials for the ADBV. Silicon is supposed to be more temperature stable of the two and remain flexible better for long oil change intervals. Premium filters often tout their silicon ADBV right on the box. Hopefully, either one will seal properly for a reasonable oil filter life, but the silicon version probably really is better. 
Some filters have the bypass valve on or near the threaded baseplate, and some have it on the opposite end - often called the "dome end" of the filter.
The advantage of a threaded end bypass  is that if and when the filter goes into bypass mode, the unfiltered oil from the oil pan is pumped around the media without first flowing past it.
When a dome end bypass opens, the oil flows past this media on the "dirty side" of the filter, there is the possibility of some of the previously captured debris being swept back into the engine oil.
I do not feel that this is not a big problem with dome end bypasses since there will still be pressure against, and usually some oil flowing through the media, tending to hold filtered debris in place.