The difference as I see it: computer science (sorry, "informatics") is a mathematical discipline, and hence tends to concern itself with, out of a given class, the minimal (and maximal, when existent) object(s). Programming is an engineering discipline, and hence tends to concern itself with, out of a given class, the intervals within that lattice that are optimal by some suitability function.

In principle, the suitability function would be evaluated over the entire lattice; in practice, that function, whether explicitly or implicitly, includes a strong weight for "distance from existing solutions". In either case, this split in focus between the interior and the boundaries of the solution space means that programmers are often highly concerned with specific details that do not even appear (because they have been abstracted away) in the objects with which informaticians work.

As an example: theory people love to use 1-ary trees (induction steps cost nothing in proofs, but cases are expensive) and they will use 2-ary trees (sometimes even without pressure to sympathize with the machine) but systems people and programmers use k-ary trees (where, if it's been determined by measurement and not by compatibility, k depends upon "the" bandwidth-delay product between the storage hierarchy levels for which the tree is optimized ... or at least what the bandwidth-delay product had been at the time of writing).