lua not handling anchors in string.find or string.match

This has been asked before at Pattern in lua with anchors not matching however I have a test case that shows that it still doesn't appear to work:

patterns = {
    'a@b',
    '^a@b',
    'a@b.com',
    'my-a@b',
    'my-a@b.com',
    'a@b.com$',
    '^this-is-my-a@b.com',
    'this-is-my-a@b.com$',
    '^this-is-my-a@b.com$',
}

test = "this-is-my-a@b.com"

for _, pattern in ipairs(patterns) do
    print(pattern .. ": " .. test .. "\n\tfind: " .. (test:find(pattern) or 'nil') .. "\n\tmatch: " .. (test:match(pattern) or 'nil'))
    print(pattern .. ": " .. test .. "\n\tfind: " .. (string.find(test, pattern) or 'nil') .. "\n\tmatch: " .. (string.match(test, pattern) or 'nil'))
end

I did the separate test:find vs string.find(test...) just to be sure there were no shenanigans.

Can someone enlighten me on how I can get my anchored patterns to work?