Are there different types of genes associated with tay-sach's?

Rarely yes: Almost all patients with tay-sach lack hexosaminidse a activity due to mutations in the hex a gene. The infantile form have less than 5% activity while the juvenile and adult forms have partial deficiencies. A very small subset of patients have normal hex a activity but have a mutation in the gm2 activator gene that codes for the intralysosomal protein, gm2 activator that degrades gangliosides.

HEXA gebe: Tay-Sachs disease is caused by mutations in one gene, the HEXA gene. There can be various mutations of that gene though. Please see this discussion: https://rarediseases.info.nih.gov/diseases/7737/tay-sachs-disease and see https://en.wikipedia.org/wiki/Tay%E2%80%93Sachs_disease