The 4-4 point is frequently and interchangeably called 'hoshi point' and less frequently 'star point'. Komoku, takamoku and mokuhazushi are frequently called '3-4 point', '4-3 point',etc. Komoku etc. is Japanese (and also in Chinese but pronounced differently) and will take some time to remember and 3-4, 4-3 points could be just confusing. 'Moku' as in komoku, takamoku, mokuhazushi originally meant 'star'. 'Ko' as in komoku means small or low in Japanese (and Chinese), 'taka' means high, and 'hazushi' means out-of-place, etc. My suggestion is:-
Call 'komoku' low-star or star-low (with or without addition of 'point')
Call 'takamoku' high-star or star-high
Call 'mokuhazushi' diagonal-star or star-diagonal
Those suggested names can be translations from Japanese and also Chinese, easy to remember, and picturesque. Comments are invited. (Gotaro)
I think these descriptions are themselves ambiguous, for example
In ancient times, 'moku' meant 'star'. Today, 'moku' does not mean 'star'.
I think this page is too Japanese-oriented. Many of the terms just give the numbered coordinates in Japanese, whith no reference to special historic meanings or particular shapes. For example gonogo, ninoichi. At the very least either English, Chinese, and Korean names should be included on this page, not just on individual pages for each move.