Species are a pure categorization method,
just like seperating a Library into book themes (fiction, nonfiction) and then in more detail
(18th century french novels and modern art poems) or such.

Evolution on Earth must have started either from some protein-balls that formed
in a specific environment or a certain base organism (maybe brought by a Komet impact)

From there on was a constant seperation into evolved buildingplans. But all came from the same source.

The reason why we have a hard time to find the "inbetween"
creatures is simply, because the fossils are rather rare
snapshots of animals and plants in a certain time.
If all creatures where ot be preserved as fossils, we would be drowning in
past-time corpses.

Also the speed of chances can either be very slow and gradual
or change quite rapitly (still takes man generations then).

Evolution will usually change little in stable times, where constantly mastering a static environment is of key.
(the current successful is then likely to be the future successful)
Evolution make rapid jumps when "catrastophies" or simply
rapit climate change appear.
Then some mutations might drastically improve the sucess,
as an adaption has a higher possible return in hard times.

So evolution needs both: static times and catastrophic changes.
then it will end up with the high veriety as we have today.