Headphones: How are different types of headphones are made or designed?

Generally speaking, headphone and loudspeaker design is a rather complex field. The transduction from electrical to mechanical and then to the acoustical domain along with their interactions are quite complex to model and the parameters that affect the various aspects of the complete system (crossover, driver, horn, box) are numerous.

That being said, it wouldn't be easy to state all of them and provide a complete presentation of the way they affect the final result. Nevertheless, the target of the design is most often, and for most applications, quite constant. Usually a perceived flat frequency response (if you see the frequency response of most headphones is not flat, but this is intended in order to cancel/counteract some phenomena such as the bass build-up or the missing fundamental due to the change from open-closed to closed-closed tube of the ear canal, etc.) is of major concern. Additionally, a good step/time response is a looked-for quality and of course, as the loudness war doesn't seem to be coming to an end anytime soon, the ability to handle (reasonably) high amounts of current and pressure levels (with a good enough sensitivity) is desired.

Now, I don't think any of the manufacturers design their products with the intention of being bass boosted. The target (frequency) response each manufacturer decides to implement may of course vary from one to the other (and even between models of the same manufacturer) and some may indeed have a somewhat more prominent low end. I don't think that this means that the intended use of a headphone model is to sound like bass boosted. Most probably the manufacturers want their products to be used in pretty much any (or at least most) application (from a certain range of applications per product of course. For example close-type headphones are mostly intended to be used in live situations where open-type in more controlled audio environments), so I believe their targets are somewhat "neutral".

Apart from the design, the user may decide to use some processing based on their preferences and/or application (type of music possibly). I don't believe there's any special design on the headphone side to accommodate the possible need for equalisation of the audio material to be reproduced though.