Past research on categorical perception of lexical tone has produced contradictory results. In Experiment 1 tonal (Mandarin, Vietnamese) and non-tonal (Australian) adults were tested for identification and discrimination on speech and non-speech (sine-wave) tone continua. Tonal language speakers' category boundaries and discrimination peaks were near the middle of the asymmetric continuum, whereas non-tonal speakers used an acoustically flat stimulus as a reference, indicating that tone space is linguistically oriented in tonal, and acoustically oriented in non-tonal language speakers. In Experiment 2, three tonal-language (Thai) groups (musicians, perfect pitch musicians, and non-musicians) were tested on two new continua represented as speech or sine-wave tones. Identification boundaries were in the middle of the continuum for most participants. In discrimination, the flat stimulus was used as a perceptual anchor, and this was independent of musical background, indicating that the musical Thai participants use the same mid-continuum strategy as the Mandarin and Vietnamese speakers in identification, but the flat no-contour strategy in discrimination. Hence, perception depends on the type of task in Thai speakers: it is linguistic in identification, but acoustic in discrimination.