Yes — 'bead chain' and 'ball chain' refer to the same chain construction: a series of spherical metal elements connected by short wire links. In fine jewelry contexts, 'bead chain' is the preferred term; 'ball chain' more commonly describes utilitarian versions in base metals used for key chains and dog tags.
The construction principle is identical: spherical elements connected by short wire connectors, creating a chain whose appearance is dominated by the smooth, round geometry of each bead or ball. The distinction is primarily one of material and context: fine jewelry bead chains in 10K, 14K, or 18K gold are crafted with precision-formed spherical beads, mirror-polished surfaces, and fine-drawn gold wire connectors. Utilitarian ball chains in stainless steel or nickel are mass-produced with less surface precision and harder, functional connectors. The geometric principle is the same; the craftsmanship and materials are entirely different. A gold bead chain in fine jewelry is to a steel ball chain as a handcrafted Italian leather shoe is to a rubber flip-flop — the same general shape, completely different in execution and quality.
When shopping for gold bead chains, the terms 'bead chain,' 'ball chain,' 'bead necklace,' and 'ball necklace' all describe the same construction. Focus on karat, bead size, gram weight, and construction quality (solid vs. hollow beads) rather than terminology, as sellers use these terms interchangeably.