Not the same rider or horse. The four horsemen represent the four stages of the Ropman empire immediately after the Revelation was written. The white horse represents the empire in its still expanding stage
This is close, I think.
Textual and historical context should inform us that the white horse is
not the horse that Jesus is riding. In Chapter 19 we read of a rider on a white horse (19:11-12). This is the victorious Christ, but does the rider of the white horse in Chapter 6 also represent Christ? In Chapter 19, John calls the rider Faithful and True, and he is accompanied by his armies, also riding white horses. In Chapter 6, the rider on the white horse has no such designation, and he is accompanied not by righteous armies but by other horsemen who deliver to the land woe upon woe. Even to a layman, a horseman who is supposed to represent righteousness must seem out of place among three horsemen who represent war, famine, and pestilence.
Barclay compares these four horsemen to the four chariots pulled by four teams of horses of Zechariah 6 that represent God’s judgment on Israel’s enemies. The white horses in Zechariah 6 and Revelation 6, like all the horses in those chapters, paint not a picture of the victorious Christ but of the terrors of the wrath of God. The white horse merely represents conquest in combat, as Revelation 6:2 implies. War, famine, and disease reign supreme in the Great Revolt, perpetrated more on the Judeans than on the Romans. The Romans emerged victorious, and when a Roman general celebrated a triumph, he paraded through the streets of the imperial city with his armies, captives, and spoils while drawn in his chariot by white horses (
https://www.studylight.org/commentaries/dsb/revelation-6.html).
In summary, the horses and their riders represent the civil war in Judea. They connote the triumph of the victorious and the misery of the losers.
The white horse signifies the Roman armies who came to conquer Judea. Rome defeated her adversaries, and so wears the crown.
The red horse signifies bloodshed, its rider instigating the civil war in which Jews slew one another. The horseman’s sword is an instrument of persecution that exacerbated the inability of the Jews to engage in commerce and sustain themselves.
The black horse signifies distress. Its rider bore a scale for rationing provisions. Scarcity debilitated the livelihood of Jerusalem’s inhabitants, but the store of wine and oil, if not depleted, may mitigate some of their suffering.
The pale horse signifies death, and with it came hades. These partners in the grim and ghastly task of annihilation wreaked finality to large segments of mankind, or the Jewish the population (a fourth of it, as John relates it) by whatever means—combat, starvation, disease. Even wild animals devoured some.
One side won; one side lost. Hence the different horses.