It comes down to part shape. Round, symmetric parts — shafts, bushings, fittings — belong on a lathe or turning center, where the part spins and the tool stays put. Prismatic, multi-sided parts — brackets, housings, plates — belong on a machining center, where the tool spins and the part is fixtured. Many parts need both; multitasking mill-turn machines combine them.
Most shops run at least one of each. Add live tooling to a lathe or a 4th axis to a mill to blur the line. Value lathes and machining centers at The Machine Blue Book.
Get a real number from a Machine Blue Book specialist — free, no obligation.