Not to turn this into an argument about definitions, but reference counting is a form of garbage collection [1]—tracing garbage collection is the one that has pauses (but of course has many advantages over reference counting).
It's not just a question of definitions: I wouldn't characterize reference counting as "striking a bargain" at all. RC is just a form of garbage collection, and in its atomic form (like in Swift) it has serious downsides relative to tracing GC. Reference counting helps latency (important in mobile, which is why Apple's choice is defensible) but it pays enormous costs in throughput when compared with tracing (not to mention the problem of cycles), so much so that tracing is usually considered the superior approach unless you have special requirements. Rust's approach of manual memory management is designed to eliminate the tradeoff by allowing prompt reclamation without all the overhead of managing reference counts, which is why it's in a separate category entirely.
