'Tercer' and 'Tercero' is like what we had in a previous lesson with 'Buen' and 'Bueno'. You use the former when it's used as an adjective before a masculine noun (el tercer hijo), and the latter is right when it's used as a noun (el tercero).
'seseo' is when one uses 's' (voiceless alveolar fricative) sound for both 's' and 'c'.
'ceceo' is when one uses 'c' (voiceless dental fricative) sound for both 's' and 'c'.
'distinccion' is when one differentiates between the two.
I had the English version of this sentence (The third) a few minutes ago and translated it to "El tercero". Go figure, my answer was marked wrong and Duo showed "La tercera" as the correct translation.