this is extra firm tofu. this is the kind of tofu you want to use to make a stir fry, or scrambled tofu. you could also use firm tofu but then it'll be a little more crumbly. if you cut extra firm tofu into cubes they won't fall apart when you cook them... unless you're really rough with it.
this is silken tofu. you can get it soft, or firm. this is where some people get confused. this is better for baking or making sauces/dips/dressings/shakes. you can make yogurt with it too. if you are really gentle with it you can cube it and add it to soups, it is especially good in miso soup. this can be bought in the fridge of the produce section, usually along with 'dessert tofu' (peach or almond flavoured, most times). or you can buy it in the box you mentioned on the shelves in the organic aisle. a lot of people like mori-nu but i don't really like it.
so in short:
if you can easily put your finger through it you have silken tofu and should use it for baking/dips/etc.
if you can squeeze it with both hands and it doesnt fall apart, you have firm tofu. this is better for a stir fry. you can change the texture by freezing it and then thawing it in a paper towel or clean cloth. wrap it up put it on a plact and put another plate with a heavy book or bowl full of water on top. leave it for about 30mins, replacing the paper/cloth as it gets soaked. this will get most of the moisture out and then the tofu will soak up more of the sauce you cook it with.
i hope this was helpful!