Tails and Cosmo are together in season 3 of Sonic X.
In the Japanese version of the second last episode, when it's up to him to fire the Cannon, Tails was extremely hesitant to do so, but with the help of Eggman's reassurance, Tails screamed "I love you, Cosmo!" just before he fired the Sonic Driver towards her and Dark Oak, and although in the English version he never bluntly used those words, it is strongly implied throughout the episode that Tails simply didn't have the courage, even at the end, to admit that he loved her. Cosmo admitted in the Japanese version that she will always love Tails before dying, while in the English version she said that will never forget him.
It mainly has a rivalry with Taiream in fandom, as people who shipped Cream and Tails together were pretty upset with the arrival of Cosmo, then afterwards many of them hated on her due to her canonical romance with Tails as there aren't any official romantic Taiream hints in the general series.
Some fanfics include Skye and Melody Prower (originally Tails and Mina Mongoose's children in Light Mobius from the canon Pre-Super Genesis Wave verse) as Tailsmo children instead. In this case, Melody is changed from a mongoose to a seedrian (common fanon term for Cosmo's species).
Both Tailsmo and Taismo are frequently used names for the ship. One name might have originated as a misspelling of the other but it is unclear if this is the case. One possibility is that the original "Taismo" was replaced with the increasingly popular "Tailsmo" due to the latter being a more seamless transition between the two characters' names.