Thanks for posting. Presenter is super annoying and takes forever to get to the point. Full on selling mode. I will summarise it for everyone : HK is a circular saw and the TS is a plunge saw (blade fully retracts). The blades are not interchangeable.
Battery saws are good for site use. No need for heavy transformer. For use in the workshop (where mine (Mafell, but similar) is used exclusively) battery confers no advantage as it is always hooked up to a dust extractor.
I think you can summarise them as HKs for rougher stuff and the TSs for anything fancy. The cut quality and dust collection on the TS saws is just better. The HKC55 could do with a few more horses but proper blade choice can mitigate that most of the time.
I don't think the OP video included the Big Daddy HK85 which is a monster of a thing. It can take a "grooving block" which does pretty clean rebates on a track up to something like 35mm deep at 16-25mm wide; all in one pass. It is about as big a circular saw as I'd like to use
The HK saws tend to be bulkier than comparable models from other manufacturers - mainly due the sole needing to be wide enough to run on a track - but the depth adjuster and plunge mechanism add to the size of the body too. They really come into their own with the FSK rails which are great for quick, precise and portable cuts. e.g. trenching things you couldn't get under a mitre saw. The depth adjustment and blade cover lever on them are the nicest I've used too, although I'm sure the Mafell KSS offerings will be better yet.