` ::When making precise comparisons between classes of entities it is customary to use precisely defined entities.  ``Set`` is a precisely defined concept, as is ``program`` for any specific programming language.  In contrast ``algorithm`` is a vague term for ``class of programs that do essentially the same thing.``  There are many notions of ``essentially the same thing,`` but the one that is assumed by and is sufficient for the statement of the Church-Turing thesis is ``accept the same set of inputs.`` ::There are various finer notions.  One much studied one is based on David Park's notion of bisimulation as strengthened by Milner.  Another is based on the distinctions between true concurrency and interleaving concurrency drawn by partial-order and higher-dimensional models of computation, both of which I have written many papers on between 1980 and the present.  Yet another is based on the concept of identification in the limit, studied by E.M. Gold and others in the 1960s and rediscovered independently by Burgin in 1983 under the name ``inductive Turing machine,`` see M. Burgin, Inductive Turing machines, Notices Acad. Sci. USSR 270 (1983) 1289-1293. ::All these refinements of the general notion of computational equivalence naturally lead to new computation classes.  However none of these new classes impact the Church-Turing thesis, which is formulated for the acceptance-based notion of equivalence.  Any discussion of violations of the thesis needs to be conducted in terms of sets, the natural semantics that goes with the thesis.  Other distinctions drawn by more refined notions of ``algorithm`` while of interest in their own right have no bearing on the thesis.     `