E-2 is the default, but not the only route
The E-2 visa is what most people mean when they talk about a Korea teaching visa, and it's tied tightly to having a bachelor's degree and a sponsoring employer — hagwon, public school via EPIK or a similar provincial programme, or occasionally a university. If you already hold an F-series visa through marriage, ancestry, or residency status, you may be able to work without a sponsoring employer's involvement in the visa itself, but eligibility rules for these are specific and worth confirming with immigration directly rather than assuming.
