Straightedge can be regarded as a ruler without any marking.
The following are exactly what a straightedge can do:

Draw a unique straight line through two distinct points

Extend a line segment arbitrarily far in both direction

Notice that it cannot be used for measuring length.

A straightedge

Compass

Compass is a V-shaped drawing tool with a sharp point on one arm and a pencil on another arm. The two arms are joined by a hinge so that the openings of the arms is adjustible.
Obviously, a compass is mainly used for constructing a circle centered at any given point with any given radius.
There are two types of compasses:

Modern compass - We can keep the opening fixed when the compass leaves the plane and carry to another location for construction.

Euclidean (or collapsible) compass - The compass "forgets" the width of the opening when the compass leaves the plane i.e. we cannot keep the opening fixed.

A real compass

Geometric Constructions

We can use the following applet to simulate geometric constructions using straightedge and compass.