No, Taiwanese citizens do not need to apply for both a visitor visa and an eTA to travel to Canada. You will need either one or the other, depending on your travel document, the country that issued it, your nationality, and how you will travel to Canada.
Taiwanese citizens can enter Canada through an online system called the Electronic Travel Authorization for Canada, or eTA, without visiting the Embassy or Consulate.
Taiwanese citizens are among the more than 50 countries that, if they register with the eTA system, are exempt from needing a visa to enter Canada, according to Canadian visa regulations.
Taiwanese travelers can enter and exit Canada as often as they please with the Canadian eTA, which is valid for five years from the date of issuance and waives the need for a visa. For Taiwanese passport holders wanting to travel, do business, or simply visit Canada, the eTA offers the easiest option.