What is the difference between "Form Controls" and "ActiveX Control" in Excel 2010?

Google is full of information on this. As Hans Passant said, Form controls are built in to Excel whereas ActiveX controls are loaded separately.

Generally you'll use Forms controls, they're simpler. ActiveX controls allow for more flexible design and should be used when the job just can't be done with a basic Forms control.

Many user's computers by default won't trust ActiveX, and it will be disabled; this sometimes needs to be manually added to the trust center. ActiveX is a microsoft-based technology and, as far as I'm aware, is not supported on the Mac. This is something you'll have to also consider, should you (or anyone you provide a workbook to) decide to use it on a Mac.

One major difference that is important to know is that ActiveX controls show up as objects that you can use in your code- try inserting an ActiveX control into a worksheet, bring up the VBA editor (ALT + F11) and you will be able to access the control programatically. You can't do this with form controls (macros must instead be explicitly assigned to each control), but form controls are a little easier to use. If you are just doing something simple, it doesn't matter which you use but for more advanced scripts ActiveX has better possibilities.

ActiveX is also more customizable.

It's also worth noting that ActiveX controls only work in Windows, whereas Form Controls will work on both Windows and MacOS versions of Excel.