When working with regression in algebra we use y=ax+b but in stats and prob we use the equation of y=b+ax, when computed using the calculator you get the same values, what is the difference between the two and why do have this difference between the te equations

I don't know what you're asking, y=ax+b is the same as y=b+ax.
IF you're asking about writing the design matrix, you can use y=ax+b
as your model, then the first column are the x's and the second column is all 1's and that works just as well.