These sites are all highly likely to be using something known as TLEs (two line element files) or "keps", which come from NORAD, based on radar observations, for their positional data.

https://www.celestrak.com/NORAD/documentation/tle-fmt.php

https://www.celestrak.com/NORAD/elements/

Anything using these TLEs should be identical.

For radio reception, if the problem wasn't pointing calibration, I suspect it was polarisation. There is ~3dB difference between 0 and 45 degrees, but ~25dB difference between 0 and 90 degrees. Therefore either use circularly polarised antennas (e.g. https://www.wimo.com/xquad-antennas_e.html) so you're never more than 45 degrees out, or if it's hand-held, simply twist the antenna for maximum signal strength. The polarisation will vary through the pass.

For some really crappy satellite positioning / radio software that everyone uses because no-one's written a better one yet, check out satpc32.