Seamless:

The term 'seamless' is used to describe a tube that has been manufactured from a solid piece of metal as opposed to a flat sheet that is rolled and welded on the seam. The tubing is created constantly working a metal billet that gets pierced through the center, and drawn into the desired dimensions and wall thicknesses.

Butted // Butting:

The process of creating varying wall thicknesses within a tube's construction. This can be done both internally, in which the external diameter does not change, as well as externally in which the internal diameter does not change. Most traditionally, this process is used to create thicker tube walls near the areas that get welded together to maintain the overall strength of the tube, while removing unnecessary material from areas that see less stress.  

Heat Treated:

This refers to using a heating process to change the properties of a metal to get a desired strength outcome. Adding extreme localized heat (welding) causes metals to become weaker than they were before that heat was applied. In order to combat that, you can either make your material thicker so that the end result is strong enough, or you can do various methods of heat treatment to keep the strength up. In steel frames, heat treatment is usually applied to specific tubes pre-welding to get the desired outcome, and is a custom recipe of what temperature, duration, and method of cooling is used. In aluminum, heat treatment is typically done to an entire frame after welding, but is more a standardized recipe to get to a specific material condition (in 6000 series alloys, commonly referred to as T4 or T6). In Titanium, there is no "normal" method because Titanium cannot be heated to high levels in the presence of oxygen, so any heat treatment has to be done in an autoclave, and is typically a secret to how it is done. So, heat treatment is not just a standardized thing, but is a common term to refer to a process that has been used to improve the strength of the frame.

Tapered:

In the context of creating metal tubes, a 'taper' refers to a tube with a diameter that has a different starting and ending diameter.

Drawn Over Mandrel (DOM):

DOM describes a cold-forming process where a tubing is pulled through a die and over a solid rod (mandrel). This process works the material in a way to refine the grain structure of the material, as well as keep tighter tolerances in the thickness of the material.

Electro-Deposition (ED) Coating:

A process in which electricity is used to apply a uniform, durable layer of protective coating to an object (both inside and out). In the case of a bicycle frame, Steel, that is typically prone to rust or corrosion can be protected when the manufacturer adds this layer of protection to the frame. Heck...sometimes you don't even need paint after a frame has been ED Coated ;)