My apologies about the clueless remark, it was uncalled for and rude. I could make a lot of excuses (I was tired, driving all day, interviewed for a new job, and had to deal with my ex all in one day, I usually try to separate events like these but not yesterday) but it wasn't necessary.
So to address the issue directly; no, headers don't have to have equal length to be called a header. The thing that distinguishes a header from a manifold is really construction. A header has individual tubes welded together on a flange, meeting in a collector, or a series of collectors, before it meets the main exhaust tube. An exhaust manifold is typically an iron casting with myriad configuration possibilities. I have seen manifolds with the equivalent of individual runners and collector-like merges on the 4A-G series engines, and I have seen simple log manifolds where all the exhaust ports are connected by a common tube much like an intake manifold.
Because the tC exhaust is constructed of stainless steel individual tubes, it is considered a header. Just like the term coilover is misused frequently, header is also misused. FYI, all McPherson strut suspensions are coilover because coilover just means the spring is concentric with the damper. Saying you want coilovers for the tC doesn't make sense, it came that way from the factory. Same with the header issue, It came that way from the factory.
The header's job is to remove exhaust gases from the combustion chamber in a controlled fashion. I think we all agree here. The part needing clarification is the backpressure issue, and the elements of the header design and how they affect the engine's ability to make power.
So, how does the engine make power? A fuel/air mixture is ignited creating a high pressure region directly above a piston which creates a force on the piston dome. If we've done everything right, the piston moves down swiftly and transfers the force to the crank. While the piston is moving downward a couple of things are happening:
1. The volume of the trapped, expanding gas is increasing
2. The heat generated by the mixture burn is being turned into kinetic energy and being absorbed by the engine's components in direct contact with the gas.
These are the two most important thermodynamic effects. So how does the header design affect this process? When the exhaust cam opens the exhaust valve, there is still pressure in the cylinder from the expanding combustion process. This is called blowdown because there is a very strong gas pulse created in the exhaust by the (usually large) pressure differential between the exhaust system and the cylinder. The ability of the exhaust system to create this pressure differential is what discriminates between good and bad.
The ideal exhaust system will provide a very low pressure somewhere in a vacuum range to extract as much of the combustion effluents as possible. If we really get it right, we'll actually be able to use this process to pull fresh intake into the cylinder at overlap (the time when the exhaust valve and intake valves are open at the same time) because we have developed a very large pressure differential between the intake manifold and the exhaust. If we get it wrong (well, maybe not wrong, but that's a different discussion), we get natural EGR (exhaust gas recirculation) because the inert exhaust gases left in the cylinder will dampen the combustion process in the next cycle.
Now to the hard question, why do people believe backpressure is necessary? Because they've read in some magazine that an oversized exhaust can negatively affect performance from a loss of backpressure. Nothing could be more inaccurately stated. As Tchi mentioned, an overly large exhaust affects exhaust velocity. One of the fundamental exhaust concepts is the exhaust is a series of pulses, not a continuous stream. Those pulses can be engineered to control exhaust pressure through the exhaust system, and pressure control for blowdown is critical to performance.
BTW, I define performance as thermal efficiency, not maximum measured power. Generally improved thermal efficiency leads to more measured power, but not always.
So our header gives us the opportunity to manage when and where high and low pressure areas exist at any given point in time. It also gives us the opportunity to optimize when blowdown occurs. If the exhaust is "restrictive" because it is designed to optimize low rpm torque, blowdown is slower to permit the pressure on the piston to remain longer. If it is "freeflowing" it is optimized to get the exhaust gases out of the cylinder as quickly as possible consistent with creating a low pressure region in the cylinder at overlap. Neither is right or wrong, they are just different for different applications. The header features most important to this part of the process are diameter and length of primary tube. Larger diameters tend to favor high rpm torque, longer primary tubes tend to favor low rpm torque. The header designer has to strike a balance between low and high rpm operation with the primary tube diameter and length.
The other thing a header does is allows the designer to use the exhaust pulses of other cylinders to affect the cylinder actually having an exhaust event. By combining primary tubes with complementary pulses, it is possible to further control the location and size of high and low pressure regions. This is sometimes called extraction. The idea is to use the exhaust pulse from another cylinder to "pull" the exhaust from the next. This is part of the theory behind 4 - 2 - 1 headers for 4 cylinder engines. By merging the complementary (360 degree apart firing events) cylinders in pairs before merging them into the final collector, the header provides better "scavenging." Scavenging is a term used to simply describe creating a very low pressure region in the combustion chamber at the right time and thereby ensuring the most complete extraction of inert exhaust gas.
Break time, this post is getting too long. I'll finish later.