Taylor series were actually discovered by
James Gregory, who
published Taylor series for functions and
Maclaurin series for tan x, sec x, arctan x and arcsec x. Independently,
Nicolaus Mercator discovered the Maclaurin series for log(1+x).
Then in 1715, Brook Taylor came along and published Methodus incrementorum directa et inversa, repeating Gregory's earlier work. However, Taylor's book was not well known until Colin Maclaurin quoted him in Treatise of Fluxions in 1742. Thus general polynomial power series came to be known as Taylor series, and Taylor series around zero came to be known as Maclaurin series.
On the other hand, Maclaurin invented the method for solving linear equations which is now called Cramer's rule.