Take me through an example of what you are talking about. Also, just so we are on the same page, could you give the definition of 'speciation' as you have used it in your last comment - thanks.
Two organisms that do not reproduce viable offspring are generally considered to be separate species. Speciation of this type has been observed both in lab experiments and in the wild. This is somewhat of a gray area, as would be expected if evolution is true, in the sense that this definition is not necessarily transitive. That is, there are examples of "ring species" where organisms of group A can breed with organisms of group B, organisms of group B can breed with organisms of group C, but organisms of groups A and C cannot interbreed. By the given definition, we would consider A and B to be the same species, B and C to be the same species, but A and C to be different species. Obviously in such cases, this definition is faulty. However this is to be expected if small variations in the genome can lead to new species formation. The "ring species" represents speciation in progress.
As far as different "kinds" not really being different, that's what evolution is really all about, namely the interrelationships of "kinds." For example, you would probably consider birds and reptiles to be different "kinds." However, if you look back far enough in the fossil record, you will find organisms that have features of both of these "kinds." This may have been an ancestral organism of the birds, and is a link showing that birds and reptiles are actually interrelated. This is the type of thing we expect to find if evolution is true, and it is simply one example, many others are out there. The whole focus of the theory of evolution is that it is possible to go from one "kind" to another via a series of many small changes, changes that are so small as to be practically unnoticeable to a lay observer. Kinds are not distinct, but rather form a continuous spectrum. The fact that they appear to be distinct to us is a consequence of the fact that most of the organisms that have ever lived are now extinct. If no organisms had ever gone extinct, then there would be no talk of distinct "kinds." Biodiversity would be seen to be a continuous, rather than a distinct phenomenon.