star - Calculating AZ and ALT from RA and DEC: values are slightly different from Stellarium

I'm developing my own planetarium software and I using Stellarium to check if the values a get from my software are correct or not.

All values are roughly equal, being different only in the seconds.

These are Stellarium coordiantes followed by my coordinates.

Note, this is a CSV txt file. I don't know if I can attached to this question so I have pasted here:

Star;RA J2000;DEC J2000;RA J2016;DEC J2016;Hour Angle;AZ;Alt.
Betelgeuse (Stellarium);5h55m10.34s;7d24m25.6s;5h56m2.38s;7d24m22.0s;23h52m25.55s;+176d38m27.3s;+55d59m52.0s
Betelgeuse (My software);5h55m10.34s;7d24m25.596s;5h56m2.32s;7d24m31.74s;23h52m25.6662s;+176d38m29.643s;+56d00m01.836s
Rigel (Stellarium);5h14m32.28s;-8d12m05.9s;5h15m18.50s;-8d11m12.8s;00h33m09.44s;+190d42m52.5s;+39d51m52.8s
Rigel (My software);5h14m32.279s;-8d12m05.9s;5h15m18.46s;-8d11m03.24s;00h33m09.5262s;+190d42m55.996s;+39d52m02.033s
Bellatrix (Stellarium);5h25m7.86s;+6d20m58.7s;5h25m59.49s;+6d21m37.1s;00h22m28.45s;+189d40m43.7s;+54d38m14.4s
Bellatrix (MySoftware);5h25m7.9s;+6d20m59s;5h25m59.42s;+6d21m46.71s;00h22m28.5662s;+189d40m48.830s;+54d38m23.685s
Mintaka (Stellarium);5h32m00.41s;-0d17m56.7s;5h32m49.55s;-0d17m27.8s;0h15m38.38s;+185d52m14.8s;+48d11m30.9s
Mintaka (MySoftware);5h32m00.42s;-0d17m56.6988s;05h32m49.51s;-0d17m18.1958s;00h15m38.4762s;+185d52m18.043s;+48d11m40.40s
Alnilam (Stellariumm);5h36m12.82s;-1d12m06.9s;5h37m01.63s;-1d11m44.00s;00h11m26.31s;+184d13m21.1s;+47d21m31.3s
Alnilam (My software);5h36m12.82s;-1d12m06.912s;5h37m01.57s;-1d11m34.2547s;00h11m26.4162s;+184d13m24.435s;+47d21m40.929s
Alnitak (Stellarium);5h40m45.54s;-1d56m33.2s;5h41m34.07s;-1d56m16.6s;00h06m53.87s;+182d30m42,7s;+46d40m01.3s
Alnitak (My software);5h40m45.55s;-1d56m33.2160s;5h41m34.03s;-1d56m06.8887;00h06m53.9562s;+182d30m45.212s;+46d40m10.931s
Saiph (Stellarium);5h47m45.40s;-9d40m10.6s;5h48m31.01s;-9d40m03.7s;23h59m56.93s;+179d59m01.5s;+38d57m56.3s
Saiph (My software);5h47m45.38s;-9d40m10.5960s;5h48m30.9500s;-9d39m54.0031s;23h59m57.0362s;+179d59m03.631s;+38d58m05.992s

Is that different a problem?

I don't know which value is the correct one (the one from Stellarium or the one from my software). The maximum difference is about 10 seconds.

And the difference between declinations (Stellarium and mine) is always greater that the difference between right ascensions.