Visa Run - When your tourist visa expires, you need to exit and re-enter the country, to renew the visa.
Visa Run - When you are using a tourist visa and get hired for a job, you might need to exit the country to make your work visa.
Visa on Arrival (VoA) - You can make your visa at the border of the country you are entering.
Electronic Travel Authority (ETA) - In Australia, you apply online and your passport number is linked to an electronic visa.

Consulate vs Embassy
Consulate is the office of the consul, an appointed officer. The office can handle minor tasks like issuing visas. There can be many consulates in a country.
Embassy is the office of the ambassador, who represents their country. There can only be one embassy in the country (which would be in the capital city). Embassies do everything the consulate does, as well as officially representing their country.