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I’m trying to understand the practical difference between a geostationary and a geosynchronous orbit for a project I’m working on. I get that one is circular and directly above the equator, but when I look at actual satellite tracking data, the distinction seems to blur in the real-world operational data.

Practically, the fixed spot in the sky is a property of the geostationary scenario: the satellite's plane is equatorial and its orbit is circular, so it can stay over one longitude. In the real world, small perturbations from Earth's shape, solar radiation pressure, and thruster jitter push it around, so operators do station keeping to hold it near that point. If you pull the orbital elements, you usually see small nonzero inclination and eccentricity creeping up, which is why the tracking data shows a tiny wobble rather than a perfect dot.

I watched a satellite with a long 24 hour clock but an incline; the ground track was a slow up and down path in the sky, not a fixed point. The 24 h period is still there, but the plane isn't equatorial, so you see a north-south drift. The blur you mention often comes from those nonzero inclination plus occasional thruster firings and measurement jitter.

Plotting over months makes the line between the two even fuzzier: you can have elliptical paths that share the same period, so perigee and apogee swing and the ground path changes shape. That combination is why some observers call it the same thing in practice, even though technically they are different kinds.

Are you looking at ground-track plots or orbital elements?

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