Here are the major differences between T12 and T13 soldering tips:
Compatibility: T12 and T13 welding heads are not interchangeable. Their exterior is different such that a T12 tip cannot be used on a T13 pad (and vice-versa).
Tip styles: T13 tips only have knife tips and horseshoe tip in common with the T12 configuration, and there are fewer shapes available for T13. The T12 iron tip has more shapes and sizes, such as: T12-D T12-K T12-B T12-I T12-JL T12-C, etc., covering horseshoe tip, knife tip, one-tip, tip angle, round/round cap or elbow type solder. Solder for other types of work process will be suitable for a limited range of jobs.
New Upgrade T13 Iron Core — Soldering iron heating core is an upgrade of T12 series, which can be customized according to new handle. This also means the T13 iron tip is likely better performing or lasting than that of a T12 iron tip.
Quality and Material: The T13 iron tip is supposed to adopt a high quality iron tip, which probably indicates its excellent performance compared with the T12 tip along with a longer life.
In summary, despite great similarity in power and thickness between the T12 & T13 soldering iron tips, these types of tips differ in compatibility, availabe shapes (and variety) and quality of the core material use.