Pages can look different in FF or IE. This can either be attributed to non-supported elements or attributes (IE does not support a lot of advanced CSS2 features and all other browsers do not support some IE proprietary tags), incorrect rendering of elements (IE refuses to fully follow the W3C standards and interprets certain -- usually more advanced -- features in its own proprietary way), browser confusion at incorrect code (if you use invalid coding techniques, browsers are left to determine how to render certain things and their "logic" can differ) or simply different default application of styles (different default paddings or margins on specific elements).
The first difference can be easily avoided. Using a syntax that is fully supported by all the modern browsers, you can make sure there will no problems with your page being displayed differently on account of unsupported things.
The second one is the most puzzling but also the most common. IE in particular renders certain things in a strange fashion and usually requires weird solutions to make it behave properly. These problems usually arise with more complex designs, so you should be ok with simpler things. Here's a nice list of these IE bugs:
The third one is quite common as well but can be easily avoided. By running your html and css through online validators, you can eliminate 99% of the problems that come from incorrect syntax. Your motto should be: do not even try to determine browser differences until you have: a) correct doctype; b) valid html; c) valid css.
The last can be a pain if you're trying to do pixel perfect designs across different browsers. IE and (mainly all) other browsers apply different default styling on certain elements, be it just different values (larger or smaller margins and paddings) or different methods to achieve the same (margin instead of padding). If you do pixel perfect design, it might be useful to begin your css by zeroing out all the margins and padding to ensure all browsers begin from the same place.
All that said, Richard is right -- make sure you test in both browsers, though I will agree with him and say that you should design in/for FireFox and check and adapt to make it work in IE as well. Because IE should not be trusted enough to expect that the website that looks good in IE will look good in other browsers.
