There is not an official way to classify cannabis. There are a couple of qualities that you can look for though, but as for one way there is not one
Indoor/Outdoor
This is just where its grown. Indoor usually caters to better quality plants, but it is not true in all cases. Seedy stuff is most likely grown outdoors. The seeds come from pollination and plants are more easily pollinated outside.
Male/Female
You are always smoking a female plant. Males are shit for smoking and the only thing they could be good for is making hemp or maybe some sort of fuel. Females if not pollinated will not have seeds and produce those crystals/trichromes that have your canniboids. If they are pollinated they will have seeds and THC percentage is much lower.
THC/Cannaboid %
Theres no way to do this at your house or tell really. In general schwag would probably have 1-2% THC. Mids would have 3-7%. Something with out seeds can have a wide range of percentages generally from 10% - 30%. Thirty percent is incredibly strong. Most hashes have on the order of 40-60%. And you could also have an Butane Honey Oil extract with 95+ % THC. These numbers are all from the top of my head. If you look up a strain guide you might be able to find them. Percentages can vary depending on the treatment of the plant.
Strains
You can find in depth information if you know what kind of strain you have. Some popular examples are White widow, Northern Lights, Jack Herer, Strawberry Cough, orange kush, G-13. The list goes on forever and new ones are made frequently. Seed banks and seed selling site have information on genetics, sativa/indica index, growth times, where to grow it, nutrient information, smell, taste, what it looks like and preferred light cycles. Heres a site
http://www.marijuana-seeds.nl/ . Keep in mind its illegal to order these in the US. They will also have this information at the cannabis clubs in california where you can buy it there. Some people just make up some kind of names for what they get without having any idea of genetics, dont be surprised if that happens. This is the best way to classify weed
Sativa:Indica Index
Most pot is not straight sativa or indica. They do exist but they are rare. For example white widow is 60:40 (sativa:indica). The only real way to know this is by getting an established strain with known genetics. You can't get this information really from any old shit you just buy
Common names
Theres nothing official about these just something you may want to call it to differentiate when your talking about what your paying for. These kind of names are very subjective as to your location and crowd. hopefully i dont get grilled for putting prices on here. please remove them if there in appropriate and once again this is off the top of my head
schwag- shitty weed/brown/dry/ lots of seeds/ compressed/ many stems >US$100 an o
mids - some seeds/ could be fluffy or compact/ maybe a small amount of crystalization $100-160 an o
nug or beasters - good weed/ no seeds/ no known genetics $250 - 400 an o
Strain name ______ - usually the best kind of stuff (probably indoor grown) you can get because it has known genetics and sativa:indica indexes $350+ an o
hydro- grown hydroponically indoors