Well I'll give you links to the features that both web hosts offer.
Hostgator:
http://www.hostgator.com/shared.shtml
Godaddy
http://www.godaddy.com/gdshop/default.asp (Select Web hosting from the hosting and servers tab, then click the link to compare plans)
These are the cheapest solutions that they have to offer I doubt you will need any extra features unless you are moderately big firm.
PHP is similar to HTML in simple terms its just more dynamic and allows you to do a little more with your website.
If you have a look on peoples websites they usually have /mypage.html
For php it will be /page.php
Its just a different format however it requires quite a lot of knowledge but both of Daddy and Gator have PHP support so when your ready and have learnt the basis of it you can perhaps integrate it into your site.
Web Terms
MySQL Database / PHPmyadmin = Complex database that is needed for blogs, forums, cms and also for storing peoples identification credentials and just general personal information. Just like a school class register at the start of the day but a little more vamped up
Python = A script that's allows you access to installing objects such as a sitemap.
SSH & SSL = Security features for looking after peoples information and protecting your visitors.
CGI = Required to install chat rooms, guest book, contact us forms.
I think those are the main ones, on Hostgator if you click the small blue question mark it tells you all about the different features.
I hope you find what you are looking for and I have'nt confused you to much.