Logo is a symbol. An iconic design that represents something. Although it's an icon for something symbolic, it doesn't mean that a logo is an icon.
At first glance, people may think there is not that much difference between a logo and an icon. After all, both are used to represent something. Most consider them one and the same. People often stumble upon the confusion between these two aspects. While logos may use the same visual vocabulary as icons, there is no doubt that logos and icons are two completely separate design disciplines requiring different tools and different mindsets.
The difference between the designers vocabulary and the clients can cause some problematic confusions.
What is a Logo?
A logo is a graphical element, with arranged typeface that together forms a trademark. It's a name, symbol, or trademark designed for easy and definite recognition, especially on a single printing plate or piece of type.
A logo is a recognizable symbol used to represent a business or an organization. Its representation of the organization may be direct, abstract or hidden. A logo must be immediately associated with the thing it represents. It taps into the organization's mindset and public image, its values and is a graphical summary of the company's brand.
There's an infinite amount of ways to think about logos and logo design.
Scalable
A logo should be completely scalable. A logo is the spearhead of a company's, or any commercial brand and any economic or non profit entity. A logo should be replicatable across many forms of media. This has great impact on the sort of mindset. A logo talks about strict vector-based result, graceful degeneration of colors all the way down to uni colors.
Without Boundaries
A logo could be anything. A logo has very little rules if compared to an icon. A logo design is not influenced by technical dimensions and other restrictions that holds it down. Its design is a completely different venue. A logo could be any shape, color or dimension. It can be as big as a banner and a billboard, and as small as a design on a business card and tattoo. Its only limit is that of the physical media that will display it.
What is an Icon?
An icon directly represents an idea, concept, operation or action. It's a visual descriptors of function; simplify or summarize an operation through a graphical representation, and relays this to the user. An icon is an image; a representation, a picture on a screen that represents a specific file, directory, window, option, or program. It's an important and enduring symbol.
Apart from any religious denotations an icon is a graphical representation of a concept or operation. We use icons to bridge the understanding of abstract analogies and practical use. Icons can be used to illustrate an entire application or individual operations within that application. In short, icons help us understand and recognize concepts that might otherwise be pretty hard to grasp.
Unscalable
Usually, icons are not made to be scaled. The idea of icons are to best convey a given message within a predetermined confined visual space. In today's iconcentric interfaces we allow for multiple variations of the same icon. The icons that are sitting in your dock most likely have atleast 5 different states embedded, making them appear crisp in all aspects of your interaction with them.
List view in OS X gives 16×16 pixel version while the dock gives the 256×256 pixel. These icons are not scalable vector, they are raster images. The designer must carefully select how to best take advantage of the canvas in any given size and more than often completely recreate the icon in those sizes.
Quadratic
Icons operate within a square canvas. How designers choose to employ that canvas is up to them, but it's restricted to that square, straight edged space. Icons are meant to fit into their little box, and they can not go outside of those boundaries. That's because they're made with technical restrictions and rules in mind. Logos don't really have these rules.
Icons are not scalable, they're made by raster imagery, born from the desire to objectify an operation or a concept within a confined visual space.
Conclusion
Although some logos use an icon to make it more distinguishable, icons are logos are completely different based on the technical aspects alone. Both may represent something, but both are two different matter that has different approach of understanding. The real difference between a logo and an icon comes in the technical aspects of the overall makeup. The tools and processes used to create both differ greatly.