To clarify things, there are now two different types of widely-accepted Braille, Original and Unified. Original has been the normal form of Braille for deccaides, and is favored by folks who graduated from school prior to 2010. Original Braille is also known as EBAE (English Braille American Edition).
Unified English Braille strives to eliminate the ambiguities that exist in some Standard Braille characters. It is quickly becoming the prefered format for students, as it is somewhat easier to learn. If you're ordering a book for a younger person, therefore, Unified English Braille may be the right choice.
In reality, when reading a novel, there are very few differences between Original and Unified Braille. So, don't worry too much about your choice here, your loved-one shouldn't have too much trouble reading either format, even if he or she is more familiar with the other choice.
Uncontracted Braille (unfortunately also called Grade 1 Braille) consists of the standard Braille alphabet, with no contractions (or abbreviations). The only people who use uncontracted Braille are those who are very new to reading by touch, or are learning English as a second language. This has nothing whatsoever to do with what grade a student is in at school.
Now because Braille books are so much larger than print ones, numerous contractions have been introduced to make them take up less space and faster to read. Contracted Braille is known as Grade 2, and is by far the most widely used. Contractions such as brl for Braille, as well as one-character symbols for common words like and, the, and which make it much faster and easier for everyone to enjoy a Braille book.
In summary, if you're ordering a Braille book as a gift for someone, and aren't sure which format to choose, remember that Standard Contracted Braille is by far the most popular. Unless your friend hasn't read more than a couple books in Braille, you're definitely safe to just stick with Contracted Braille.
One last idea: you could pick up a Grade 2 Braille Contractions Booklet This nifty booklet lists every possible Grade 2 contraction and what it stands for. So if your friend hasn't been reading Grade 2 Braille for years and years, he or she will always have this handy little booklet to look up a particularly puzzling symbol now and then.