My Grandma taught me the difference between the Chrysanthemum species. She didn't know these scientific names, but she knew what their popular names were. In our country, the large flowered mums are called chrysanthemums and the small flowered are called small bush plants. When I first started to create my own garden I wanted to have mums in it, in the memory of my beloved grandma. That's why the first perennials I planted in my garden were a few white daisy mums. At first I didn't know much about them, but watching the workers in the park nearby I've learned a lot, and not only about mums. This is how I've found out they are perennials , very resistant to drought . In my garden I'm watering them everyday, all summer, but in the park they were surviving without regular watering so they never appeared to be thriving. They were starting to grow better in the fall, when we start getting rain. Nowadays they don't plant them until the fall, when they are in full bloom.
Mum's botanical name is Chrysanthemum and it is a perennial plant, from the Asteraceae family. It is related to aster, dahlia, zinnia, calendula and also to camomile. From what I've read about this plant, it is originally from China and has been used (and still is) for cooking in China and Japan. Later it was introduced to Europe too. Many hibrids have been created since then, but the most important is Chrysanthemum morifolium. The cultivars are named after their blooms color and form.
The mums are divided in 13 categories after the form of their blooms, such as irregular incurve, regular incurve, pompon, intermediate curve, decorative, spoon, quill, spider etc.  My friend Jules(Singingwolf) has many species growing in her garden and has graciously allowed me to use her photos for this article.
'Warm Megan' 'Debonair' 'Wildberry'
'Bold Vanessa' 'Wanda' 'Padre'
'Anna' 'Duchess of Edinburgh' 'Bonnie'
'Mamoth Red Daisy' 'Frosty Jeanette' 'Alisha'
SPOON MUMS CUSHION MUMS
IRREGULAR INCURVE MUMS
'Snowdon white 'Crimson Tide' 'Flashy Gretchen'
I've found out a very interesting thing about the Chrysanthemum flower, also called floret, that it is formed of two kinds of flowers : the ray florets and the disk florets. The ray florets are the petals, while the disk florets are very tiny flowers in the middle of each bloom; these are the real flowers which have both male and female reproductive organs.
The biggest Chrysanthemum, grown as a single flower on the stem is called 'ogiku' in Japanese . The technique for getting such a huge flower is very interesting. It consists in pinching off the new growth from a leaf, the so-called suckers (same as for tomatoes) whenever they appear. Also, staking is necessary before the plant starts budding to prevent breaking their stalk, either because of the heavy burden of the flower or to strong winds. When the first bud pops up, it has to be pinched off, encouraging another new bud to grow. This way the flower will be real huge.
I always tie up the mum stalks by the fence. Mine are a bit crowded, although I've divided them every spring, after the first sprouts appeared. I've never tried to grow a large flower, but I will have to do that next year and also try pinching, which should be fun. I've tried that with my hibiscus plants and it works, meaning they have more buds and are bushier.
'Crimson Tide' 'Crimson Tide' bud
'Flashy Gretchen' 'Flashy Gretchen' bud
In our country people are growing mums in their gardens and they are coming out every spring, no matter how hard the winter has been. Last November, my mom gave me 3 mums for my garden. They are also Chrysanthemum x morifolium species the Decorative genus. I didn't know what to do with them because it was too late for planting in the garden, but it would have also been too warm inside my home for them. Not to mention I didn't need 3 pots more , added to the 100 and such I already had! My friends adviced me not to plant them because they wouldn't survive during winter freeze, but if I was to do so , I should better cover them with some mulch. I followed their advice and planted the mums in my garden, then covered them with some mowed grass. I was a bit worried they wouldn't survive after such deep freezes and so much snow we had, but they did and now they are blooming and adding more colors to my garden ! They are from the small bush plants category, as we're calling them here in Romania.
'Ginger' 'Pam' 'Kagaribi'
First mums blooming in my garden are the daisy-like varieties. First are the white Chrysanthemums, also called Daisy Mums 'Tracy', which start blooming in mid October. A week later, the cheerful dark red Daisy Mums 'Alisha' are also starting to bloom. Later they are changing colors to pink and dark pink.
These decorative mums 'Crazy Victoria' are always blooming next, in late October. They are showing rusty buds when first blooming, then change to variagated rusty and "explode" to a yellow halo around the daisy eye.
These yellow mum cultivars are early blooming mums, starting early September. 'Bright Gretchen' is blooming in August , looking so lonely between the morning glories and sunflowers!
'Sunny Tracy' 'Golden Marilyn' 'Bright Gretchen'
This daisy-like plant which I found growing in my garden last summer, is also a Chrysanthemum species. It grows on the field around my house and the wind must have brought some seeds into my garden. It is called Pyrethrum or Tanacetum(Chrysanthemum) cinerariifolium and its flowers are used for making a very effective insecticide . They are used as companion plants to repel pests from the nearby plants. They repel many insects, such as leafhoppers, spider mites, aphids, ticks or pickleworms and cabbage worms. 
, - http://en.wikipedia.org/wiki/Chrysanthemum
 - http://en.wikipedia.org/wiki/Pyrethrum