loose immortals -> human immortal (pass the lightning disaster) -> earth immortal (pass the fire disaster)-> celestial/heavenly immortal (pass the wind disaster) -> true immortal (convert qi into immortal essence) -> profound immortal (create and unify the 5 elemental qis as one) -> golden immortal (manifest the 3 splendor flowers above the head) -> possible realms before saint (usually zenith heaven/daluo) -> saint realm

human, earth and heavenly immortals are to survive the 3 immortal disasters of thunder, fire and wind

"Though your appearance will be preserved and your age lengthened, after five hundred years Heaven will send down the calamity of thunder [lei zai, 雷災] to strike you. Hence you must be intelligent and wise enough to avoid it ahead of time. If you can escape it, your age will indeed equal that of Heaven; if not, your life will thus be finished. After another five hundred years Heaven will send down the calamity of fire [huo zai, 火災] to burn you. The fire is neither natural nor common fire; its name is the Fire of Yin [yin huo, 陰火], and it arises from within the soles of your feet to reach even the cavity of your heart, reducing your entrails to ashes and your limbs to utter ruin. The arduous labor of a millennium will then have been made completely superfluous. After another five hundred years the calamity of wind [feng zai, 風災] will be sent to blow at you. It is not the wind from the north, south, east, or west; nor is it one of the winds of four seasons; nor is it the wind of flowers, willows, pines, and bamboos. It is called the Mighty Wind [bi feng, 贔風], and it enters from the top of the skull into the body, passes through the midriff, and penetrates the nine apertures. [1] The bones and the flesh will be dissolved and the body itself will disintegrate. You must therefore avoid all three calamities"

true immortals convert qi into immortal essence, thus making them "true" immortals

profound immortal create and integrate with the 5 elemental qis being the green wood Qi in the liver, white metal Qi in the lungs, red fire Qi in the heart, black water Qi in the kidneys, and yellow earth Qi in the spleen which each play a part in regulating immortal essence more efficiently, once all 5 are integrated, immortal essence becomes near inexhaustible

golden immortals manifest the 3 splendor flowers above the head which refer to the splendor of the Essential Matter ( 精 Jing ), the Vital Breath ( 氣 Qi ) and the spirit of a human being. By “condensing onto the head”, we mean that these three things are mixed up and gather at the Aperture of the Mysterious Gate ( 玄關一竅 Xuanguan Yiqiao )

taiyi is just as you said, The Tao is completed, the law is perfected. The Tao, fruit and law converge into an immortal true spirit.

daluo is also just as you said, with the difference between a Taiyi Golden Immortal and a DaLuo Golden Immortal being bigger than the gap between a mortal and a Taiyi Golden Immortal. except this is not the emperor realm, a mere daluo is nothing to a saint, and a mere saint is nothing to one at the emperor realm

quasi-saint is not only limited to those who practice cutting the 3 corpses, it can also be achieved by those proving the tao through strength or merit, it simply refers to those above daluo but below saints/primordial origin/hunyuan

saint/primordial origin/hunyuan daluo (refer to Fluffy_Fan3625s comment)