I'm trying to understand the differences between obliquity and inclination when it comes to a system of a planet orbiting a star. From what I understand, obliquity is the angle between the orbital plane of the planet and its axis of rotation. However, when I am reading about inclination - it seems that it is very similar. Can someone please clarify the difference between the two?
The inclination is the angle between the plane of the orbit and some other standard reference plane. For orbits around the sun, the reference plane is usually chosen to be the ecliptic, that is the plane of the Earth's orbit (so the inclination of the Earth's orbit is zero) For orbits around the Earth, the reference plane is chosen to be the plane of the Earth's equator.
For exo-planets, the reference plane is the plane that is perpendicular to the line of sight from the sun to the star.
I emphasise the word "chosen" because the choice of reference plane is in some sense arbitrary. It is like choosing a frame of reference to locate the orbit of the planet. Strictly one should always say that the inclination is $i$ degrees relative to the plane of the ecliptic (or the equator etc), but typically the reference frame is understood from the context.
Unlike the obliquity, the inclination does not depend on the rotation of the planet in any way.