buckle up at-sushi (essay under cut)
the mainland asian tiger (P. t. tigris) is the largest member of the "big cat family". it is a sister species to snow leopards, and was first described in 1758. im working off the assumption that yours is a Siberian tiger (P. t. attaica) which inhabits north eastern china, north korea, and parts of siberia. this places you in the family Felidae and the genus Panthera (species Panthera tigris).
the common house cat (F. c. domesticus) was also given its scientific name in 1758. it is in the family Felidae and the genus Felis (species Felis catus). it was given the subspecies Felis catus domesticus in 1777.
when Panthera tigris was first described in in 1758, it held the scientific name Felis tigris, as Panthera had not been classified as its own genus. it was added to the genus Panthera in 1929. genus Panthera refers to a lineage of megafauna which distinguishes them from genus Felis.
the family Felidae which both genuses fall under has a common ancestor dating back 10-15 million years. the genus Felis is suspected to have branched off from Panthera around 7 million years ago based on fossil evidence and mitochondrial DNA. genus Felis was created through artificial selection (selective breeding) to make them smaller, resulting in not only the common house cat, but species such as the black footed cat (smallest in the genus Felis).
Panthera and Felis are used almost exclusively to describe difference in size, and at one point, all cat species (including the siberian tiger) were classified under genus Felis.
this means, in short, that you are taxonomically, genetically, and historically, a cat. :)