The typical conception of Algebra is largely based on the educational definition encountered by people in their schooling, which will posit algebra as the branch of mathematics that allows for the substitution of letters for numbers, and contrast it with arithmetic.
While this differentiation between Algebra and arithmetic decreases in higher level mathematics because they usually always entail alphanumeric representations of values.
The contrast between algebra and geometry, however, becomes more marked at higher levels of mathematics.
Geometry is presented as largely focused on shapes, and their dimensional variants, and concepts/processes such as rotations and transformations.
What's particularly unique about geometry is that it is inherently visual.
However this does not absolve geometry of relying on symbolic manipulations, or representations, and conversely, solutions to algebraic problems can be attained by visualizing them geometrically.
One example of visualizing an algebraic problem is to consider how to justify the rule that if a and b are positive integers, then ab=ba.
This is the commutative property at play.
This problem can be solved purely logically, but it is much easier to imagine a rectangular array of a rows, and b columns, and observe that swapping the values of a and b don't change the area of the rectangle.
On the other hand, it turns out that a great way to solve problems that are geometric in nature, is to convert them into algebraic problems. The most well known technique for doing so is to use cartesian coordinates.