Yes, this is a common question among beginners and you should understand this basic theory well and quickly!
Read this article I posted on my sax articles section:
https://howtoplaysaxophone.org/saxophone-keys

Let me know if anything is still not clear.
Johnny

Hi, great web site.
I understand scales from playing the guitar for quite a few years and just got an alto sax in Eb.
I understand if a song is in the guitar or piano key of E I am actually playing in C#. on the sax, a minor third down from concert pitch.
But when I play along to tracks in E piano/guitar key, I find that I am playing in G blues on the saxophone.
Surely it should be C# blues.
It is as though I’m playing a minor 3rd up not down from concert pitch. It is the same for other keys e.g. D blues guitar is F blues on alto
How can this be? I know the backing tracks are in E, A or B.

Thanks for the speedy reply.
I thought I must be doing something wrong.

Yes! Here’s a couple paragraphs taken from the new beginners saxophone book I’m working on that explain it:

The mouthpiece slides directly onto the corked tip of the sax neck. If it does not slide on easily you can apply some cork grease which either came with your sax or you can get at a music store. Slide the mouthpiece about half way onto the cork. So if your cork is about an inch and a half in length as most are, the mouthpiece should cover 3/4 inches of the cork.

Tuning your sax

You can tune your saxophone by pushing the mouthpiece further in on the cork, or pulling it out closer to the tip of the neck. Pushing it in further will make the sax sound sharper and pulling it out will make it sound flatter. You don’t need to worry about the tuning very much until you’re playing with others. At this point just keep the mouthpiece about half way on the cork because having it extremely too far in or too far out will make the sax be out of tune with itself.

well, like to help you but you didn’t leave a link for any song!