Rashi comments on the apparent discrepancy between numbers
FOUR HUNDRED AND THIRTY YEARS — Altogether from the birth of Isaac until now were 400 years, and we must reckon from that event, for only from the time when Abraham had offspring from Sarah could the prophecy (Genesis 15:13) “Thy offspring shall be a stranger” be fulfilled; and there had been 30 years since that decree made at “the convenant between the parts” until the birth of Isaac. It is impossible to say that this means that they were 430 years in the land of Egypt alone, for Kohath was one of those who came into Egypt with Jacob (Genesis 46:11); go and reckon all his years and all the years of Amram his son and the whole eighty years of Moses, the latter’s son, until the Exodus and you will not find that they total to so many; and you must admit that Kohath had already lived many years before he went down to Egypt, and that many of Amram’s years are included in the years of his father Kohath, and that many of the 80 years of Moses are included in the years of his father Amram, so that you see that you will not find 400 years from the time of Israel’s coming into Egypt until the Exodus. You are compelled to admit, even though unwillingly, that the other settlements which the patriarchs made in lands other than Egypt come also under the name of “sojourning as a stranger” (גרות), including also that at Hebron, even though it was in Canaan itself, because it is said, (Genesis 35:27) “[Hebron] where Abraham and Isaac sojourned”, and it says, (Exodus 6:4) “[the land Canaan], the land of their sojournings wherein they sojourned”. Consequently you must necessarily say that the prophecy, “thy offspring shall be strangers… [four hundred years]” began only from the time when he had offspring. And only if you reckon the 400 years from the birth of Isaac will you find that from the time they came into Egypt until the time they left it, was 210 years (as alluded to in Genesis 15:13). This was one of the passages which they altered for king Ptolemy (Mekhilta d'Rabbi Yishmael 12:40; Megillah 9a).
The Ibn Ezra explains the 430 as
מיום שיצא אברהם אביהם מארץ מולדתו
From the day when Avraham Avinu left the land of his birth.
The Sforno wrotes,
the sum of 430 is arrived at by commencing the count from the time G’d took Avraham out of Ur Casdim in order to conclude the covenant of the pieces with him. During that conversation with Avraham, G’d had specifically taken credit for taking Avraham out of Ur Casdim, (generally understood as saving him from the fire of Nimrod’s furnace when Avraham had been a voluntary martyr for his belief in the G’d of heaven. Genesis 15,7) This is the reason why the author of Seder Olam, an ancient historical text, describes Avraham as having been 70 years old at that time.
There are many other explanations and computations details the commentators' various positions on exactly what each of the numbers refers to and when that particular measure starts and stops.
Check through the commentaries at https://www.sefaria.org/Exodus.12.40?lang=bi&with=Commentary&lang2=en
Note -- this answers the WHAT in your question, but not the underlying "why" in your title -- why the text would be imprecise, or confusingly precise is a separate question.