In considering different types of greeting cards, the most basic decision is do you want a humorous card or a serious card? For nearly any occasion with the exception of condolence cards, you'll have that choice.
If the card you wish to get will be serious, there are subcategories here as well. Heartfelt greeting cards that sound as though you sat down and wrote your innermost thoughts; cards with rhyming poetry; or religious cards, conveying the message in a tone of spirituality.
There are a myriad of different types of greeting cards, including cards that are blank inside so that you can write your own message. Some have funny photos of animals, or computer generated graphics depicting impossible animals. Others are of beautiful scenery or unique artwork. Some use photography in unique ways to look extremely old or to depict scenes or characters from classic movies.
For a completely different type of greeting card, you can choose handmade cards individually packaged in cellophane with the envelope. These cards are highly artistic, normally cost a little more, and are usually found at bookstores. They are generally blank inside. However, if you aren't good at writing you can always buy a second greeting card that says something nice inside, then paste the second card inside of the first. When you open the homemade card, you'll see the inside of the second card. Just make sure the second card is smaller so you don't have to cut it, as it will look better that way. Use rubber cement rather than glue or paste as it won't bleed through the paper or change its color.
There are different types of greeting cards for every occasion. Birthday (including specialty milestone cards and belated), wedding, new-baby, anniversary, graduation, bar mitzvah, first communion, get well cards, retirement, congratulations (could be for a new job, new home, or any personal accomplishment), apologies, friendship, I-miss-you, romantic, and of course holiday cards including Mother's Day and Father's Day. There are even cards "from the dog" (normally for birthdays or Mother's Day/Father's Day).
For familial occasions like birthdays and anniversaries, greeting cards are broken into further categories based on who is giving the card. "To Mom From Son" or "To Father From Daughter" are two examples. There are also cards "from both of us" which could be given from siblings to parents. Generic categories can be given by anyone.
No matter what your style and bent, the extreme diversity and choice among the different types of greeting cards is bound to satisfy your needs and even delight them. Not only might you find the perfect card, you just might find two.