Does this always mean an on-and-off relationship?

Not always, though the on-and-off shape is what the axis produces when nobody names it. Named, it becomes a preference two people can build around, which is a different thing from a cycle they keep rediscovering.

Am I the restless one or the one being left?

A general description cannot say, and the honest answer is that most people carrying this have occupied both ends at different times. The position turns out to be more portable than it feels from inside any single relationship.

How is this different from Venus square Uranus?

The square keeps both appetites inside one person, where they collide in the same moment. The opposition divides them between two people, so the collision becomes a relationship rather than a mood.

Aspect

Venus opposition Uranus

Venus opposition Uranus splits a single argument between two people. Closeness sits at one end of the axis and room to move sits at the other, and instead of being held together they get handed out — one person becomes the one who stays and the other becomes the one who leaves.

The part worth knowing is that the assignment is not fixed. It reverses, usually without discussion, and usually shortly after the other person accepts it.

Roles that swap without notice

An opposition faces two bodies across the chart, and what a chart does not live from one end it tends to meet from the other. The two ends here are not equally comfortable to occupy, so one gets lived and one gets met — and the one that gets met arrives wearing a person.

Uranus is an outer body, slow, and shared across an age group, so its sign describes a generation rather than a person. What is read from it at this end of the axis is therefore not a quality belonging to either party. It is a pressure applied to the pair: the arrangement keeps being tested, and the test usually takes the form of somebody needing to be elsewhere.

The reversal is the signature. Pursue, and the far end becomes unavailable. Stop pursuing, and it comes back. Both people can experience themselves as the reasonable one throughout, and both accounts stand, because it is the position rather than the person that is doing the talking.

How it tends to show up

Relationships that run warm across a distance and cool on arrival.

Being the steady one in one attachment and the restless one in the next, with no sense of having changed.

Ultimatums that reliably produce the opposite of what they ask for.

An attraction to people who are visibly on their way somewhere, and a quiet expectation of being left behind.

What changes the reading

The opposition is granted the widest margin the scheme allows, shared with the conjunction, so a great many charts hold one. The close ones are the ones that behave like the description.

Uranus occupies a sign for years at a time, so the sign is generational. What is personal is the house at each end — one of them says where the room is wanted, the other where it is missed.

A chart with strong contacts to Venus from elsewhere can hold both ends at once, and that is what turns this from a pattern between two people into a negotiation inside one.

Questions

Does this always mean an on-and-off relationship?: Not always, though the on-and-off shape is what the axis produces when nobody names it. Named, it becomes a preference two people can build around, which is a different thing from a cycle they keep rediscovering.
Am I the restless one or the one being left?: A general description cannot say, and the honest answer is that most people carrying this have occupied both ends at different times. The position turns out to be more portable than it feels from inside any single relationship.
How is this different from Venus square Uranus?: The square keeps both appetites inside one person, where they collide in the same moment. The opposition divides them between two people, so the collision becomes a relationship rather than a mood.