Hi,
There are TWO plants that people call tansy
Senecio jacobaea (tansy ragwort) and
Tanacetum vulgare (common tansy). In some areas they are both considered noxious weeds. Here in the Fraser Valley, tansy ragwort is considered a noxious weed. This is due to the fact that it makes toxins which can eventually kill livestock, as well as being allergenic (the pollen is a common cause of hayfever). Plus it spreads like crazy (and so does common tansy, which is why it is a noxious weed in some other areas). They do not however, have any rhizomes or anything like that to worry about. They spread by making millions of seeds that float on the wind and get everywhere.
The most obvious difference between the two is that the flower of the common tansy has no 'petals' and appears to be a yellow button, while the flower of tansy ragwort does have 'petals' (technically, ray florets).
See these links:
tansy ragwort:
http://plants.usda.gov/cgi_bin/plant...gi?symbol=SEJA
http://www.fvrd.com/weeds_appearance.php
common tansy:
http://plants.usda.gov/cgi_bin/plant...gi?symbol=TAVU
