Is SQL the same as MYSQL? If not- what s the difference?

can some one please help me create a user data base and admin panel mysql wont work on my pc some reason its a vista i tried numerous times so im helping some one can just help me make a data base feel free to email or im me

I know this has been asked before but I also have certain requests.
-Uses Paypal
-Bills Monthly (ONLY)
-Cheap (under $10 a month)
-Allows PHP- MYSQL- and mass emailing
-Decent amount of space
-No popups
-Little or no lag
-No ADs

If you give me a site that I can use- you will get your 10 points =)

I googled for hours and I still can t find how to log in as a user other than root. Plus- all the things I have read show the thing on the left as being "shell>" at first- but when I start- it just says "Enter Password". Even w3school s hello world didn t help because I DON T EVEN KNOW WHAT MY USERNAME IS. I have never felt so stupid in my life- and this was also the first time I have ever used "all caps" when writing a phrase. By the way- I have php and apache working perfectly- just not with mysql.
I can login fine- but I cant change users.

I m trying to learn how Php and MySql work. I ve got a book that I m working through- but I have questions about why they use the things they do and why it all works the way it does. Is there anyone out there who would be willing to email me for a while- while I ask questions that I come up with? If so- please email me! Thanks!! :o)

I have read that indexes can help speed up MySQL databases because- instead of looking through all the records- MySQL jumps straight to the ones it needs- saving.

Unfortunately- this comes at a catch because if you re constantly changing your database (inserting- updating- deleting)- then this could have a negative impact on performance.

My question is: if I implement indexes in my database- would this have a positive or negative impact on my site- all things considered?