Calcining and pyrolyzing are different processes and reactions but both can be done in an indirect fired rotary dryer with typically the same type of feed and discharge systems. The primary difference in equipment occurs outside the “reactor” or “kiln” which is the indirectly heated dryer.

Calcination is the process of thermally treating a chemical compound with a restricted supply of oxygen at temperatures lower than the melting point of the compound. The term originally was derived from a Latin word and specifically referred to treating limestone to yield quicklime (calcium oxide) but the term has been watered down to now be used to refer to thermally treating or decomposing a number of ores and compounds. Some vertical brick lines kilns are used for large limestone particles but horizontal rotary kilns are used for the bulk of limestone calcination.

Unacademy lists the following as typical examples of thermal treatment in a calciner:

Limestone calcination – entails the breakdown of carbonate ores and the removal of carbon dioxide.
Calcination of bauxite and gypsum – requires the elimination of water vapour from crystallisation.
The breakdown of volatile components in raw petroleum coke
Making rutile by anatase or devitrification of glass materials.
Zeolit synthesis with ammonium ions eliminated.
Anhydrous alumina is left behind when bauxite is calcined and the water is removed.

https://unacademy.com/content/jee/study-material/chemistry/calcination-reactions/

Pyrolysis also occurs in an indirect fired rotary dryer by heat treating at high temperatures but requires an oxygen deficient environment due to the generation of syngas in the process. The indirect application of heat chemically decomposes organic materials. Each organic material reacts differently at increasing temperatures and a pyrolizer can be used for multiple processes, Fox example the process on wood to create charcoal or biochar as a desired end product also creates biogas.

Britannica lists numerous examples of pyrolysis in an indirect heated rotary dryer used as a pyrolysis unit:

extracting materials from goods such as vehicle tires to create carbon black and syngas.
removing organic contaminants from soils and oily sludges.
creating biofuel from crops and waste products.
removing organic contaminants sewage sludge to make heavy metals remaining in the sludge inert, which allows the sludge to be used safely as fertilizer.
Pyrolyzing biomass materials such as wood and sugarcane bagasse for producing biochar and gases.

https://www.britannica.com/science/pyrolysis Vulcan Drying Systems has been designing, manufacturing and producing calciners and indirect fired rotary dryers for pyrolysis for a number of processes. The centerpiece is the rotary dryer and insulated heat chamber with a series of burners used to create heat zones for pinpoint control of the process throughout the length of the kiln drum cylinder. A number of different fuel sources can be used for generation of heat, including the reuse of the syngas or condensed liquid gas from the process. The calcining process may use a high temperature baghouse or a scrubber or series of scrubbers as air pollution control while a pyrolysis unit typically utilizes a series of scrubbers to cool and condense the gases as well as treat any volatiles released. A thermal oxidizer can be added to thermally destroy uncondensed gases.