The fact that we classify different distinct species at all means it is a step function, not analog.
No, there are many creatures where differences are small enough that scientists debate whether a certain branch is just another breed (i.e., dogs), or separate sub-species, species, genus, etc.
The criteria they establish for these various sub-groupings are more-or-less arbitrary and may not, historically, have been consistently applied.
That's why we can see the example of Polar Bears, once classified as a separate genus, now reduced to just another species within the Ursus genus.
That change was caused, among other reasons, by the discovery that Polar and Brown Bears can and occasionally do interbreed in nature.
Another example is Neanderthals, once classified as a separate species, now considered just a sub-species, along with some others (i.e., "Hobbits") of Homo Sapiens.
One reason is the discovery that, ahem, some of us do carry a few Neanderthal genes -- who would have thunk it, Neanderthals in our wood piles? ;-)
Point is: these classifications are more-or-less arbitrary and subject to change as new data becomes available.
So speciation is strictly, in your term, "analog" -- there's nothing "step" about it.