Is the 2nd death anniversary also called barsi?

No. The term Barsi specifically refers to the first death anniversary — the Abdika Shradh of the first year. It is the only annual ceremony that includes Sapindikarana, which marks the soul permanent transition from the Preta state to the Pitru Gana. From the second year onward, the same annual tithi ceremony is called Varshik Parvana Shradh. Its structure also changes: the Ekodishta form of offering directed at one soul ends, and all future Shradhs include the deceased as part of the three-generation Parvana collective. The Garuda Purana makes this distinction clear — the soul has already been elevated and no longer receives individual Ekodishta rites.