Pretty interesting that the Chorda is from its own kingdom, neither plant nor animal? Going to have to read more on this.
Yeah, it goes by different names. These days folks I trust call it the Chromalveolata and it includes dinoflagellates, ciliates, the causal agent for malaria (which is a degraded alga if you ask me), water molds, diatoms and a bunch of other little brownish-yellowish-greenish things, and the brown algae including kelps.
A good source for algal taxonomy (the best, in my professional view) is www.algaebase.org. If you enter Chorda as the genus or Chorda filum as the species, then click the appropriate link, it spits out a reliable taxonomy among lots of other info.