Well, mostly the difference has to do with how you plan to use your logo. Here are simple explanations with samples:
Logotype / Word Mark
This type of logo would be best suited for a company where signage plays a huge roll in their brand visibility. Another reason a company might want a logotype or word mark logo is its placement among other busy content that is regularly seen by the customer or even just brand simplicity.
Iconic / Symbolic
Iconic or symbolic logos really work best for well established brands. This type of logo is great for use on products and also consistency for a brand within a brand.
This is probably the most common type of logo because it adds an extra dose of recognition and insight into a brand. In various cases, the symbolic piece can even be used alone.
Emblems are all encompassing and are sometimes used as a complimentary piece to a brand depending on its use. Most emblems are used as a seal or object of its own for placement on a product.