Most of the types you list are not "types of logo design."
Logos ("marks" is the better and more general term) fall into only three major categories:
- A logo is a graphic, abstract or illustrative, that uniquely identifies an entity such as an organization or project:
- A logotype (sometimes called a "lettermark") is a mark created from a few letters, usually custom drawn and often combined with some kind of graphic (this image courtesy of katielily.wordpress.com):
- A wordmark is a mark consisting only of type, usually the name of the organization it represents, often in a custom or modified typeface:
The dividing line between a logotype and a wordmark is slightly fuzzy, because a logotype (the IBM and FedEx logotypes are good examples) can also be the name of the company. The generally accepted definition is that a wordmark contains one or more actual words (Microsoft's wordmark).
All the rest of your "types" are simply different styles or fashions. Until the Chase Bank logo, virtually all logos were representational or illustrative in some way. Paul Rand's original UPS logo included a knot of string, for example, and the current logo is clearly representational (although it violates one of the canons of logo design, to the intense irritation of Paul Rand fans):
Fashion, far more than most of us admit, is technology-driven. "Because I can" is the unstated reason for many a poorly-conceived logo. The wealth of 3D-esque, gradient- and shading-filled logos that are meaningless or indecipherable when reduced to pure black and white is testament to this.
There are rules about designing a mark or logo:
It must look good as a flat monochrome graphic. This is the cardinal rule. Variations on the theme can introduce color and/or gradients (see the VW logotype above), but if it doesn't look good monochrome, everything else is putting lipstick on a garden slug.
Simple is better. If a logo has fine detail, you will have to create several versions for viewing at different sizes.
It must look strong reversed out of a black background. This is a corollary of the first rule. Both rules force you to create a design that is graphically strong enough to work as a badge for the client.
It must be scalable. The nightmare of inheriting a "logo" "designed" by "the guy/girl who did our website" is that it's almost always a small png or a jpeg, unusable for any other purpose than a web page.
There are also rules about what to avoid.
You have to know what they are before you can break them with impunity.
Don't confuse fashion trends with basic technique. Both have their place in your toolbox, but the basics are infinitely more important.