CASify
What both can do
Draw functions, make tables of values, find intersections and zeros graphically, do statistics, analyze data, run regressions. That's plenty for a large part of what you do in class, and it's exactly why the graphing calculator was the standard for years.
What only a CAS can do
Simplify or factor an expression. Solve an equation for a variable, even when there are parameters in it. Differentiate and integrate exactly. Keep working with fractions and roots without rounding.
The practical difference shows up with maximum, minimum and inflection points. With a graphing calculator you draw the graph and read off an approximate value that's right to two or three decimal places. With a CAS you differentiate, set it to zero, solve and get the exact value. In a test that asks for the exact position, that makes a real difference.
How to tell which one you have
On the TI-Nspire, it's in the name. The TI-Nspire CX II is the graphing calculator. The TI-Nspire CX II CAS is the computer algebra system. In Europe the two are called the CX II-T and the CX II-T CAS, and they work exactly the same way. The two calculators look almost identical, and the word CAS at the end of the name on the case is the only visible difference.
Other manufacturers use different names, but the idea is the same. At Casio, the fx-CG50 is the graphing calculator without CAS, while the ClassPad has a CAS. Older TI models like the TI-89 have one too.
If you're not sure, there's a test that works on any calculator. Type in the square root of 2 and press enter. If you see √2, you have a CAS. If you see 1.414213562, you don't.
Which one do you need?
The one your school tells you to get. It's not a matter of taste. Your school or exam board decides which type of calculator is allowed in your final exams, and your school then picks a specific model.
In some places the rules have been moving away from graphing calculators and toward CAS for a few years now. If you're in lower secondary school and need to buy a calculator, ask your maths department what will apply to your year in the final exams. A calculator easily lasts six years. The rules change faster.