To complement Rath_ reply, let me show you how your private address changes based on the order of your seed phrase. Let's assume the following:
- we are using the BIP39 Word list[1] to choose our seed words
- We are going to "generate" 12 words
With these assumptions, here's what we got:
tide recipe tool client camp clerk maze change nephew destroy elbow loud
As you may know, the seed phrases are just a more convinent way to represent your Private Key, meaning that behind these carefully placed seed words is a private key, which is the "master" key of your wallet and that it will be used to generate all your addresses. If we use a tool that allows us to see the private key "behind" those seed phrases - such as TP's Brainwallet[2] - we get the following private key (based on the previous seed phrases):
218A23AEC2D8590C94D29E561D7BE734A696F5FA1ACD77A3B85321536D624704
This generates the following address:
1HGTrcYytcf6KzGeN9Qu2VQ7HMmkBUNLyi
However, if I just switch the order of the first and the last word in my previous list like this:
loud recipe tool client camp clerk maze change nephew destroy elbow tide
We get a totally different private key:
0E424F2BBF5C82CE2A5EBCBFA3C1196988F245F55A92175F058390B1DB4D0326
With a totally different address:
18Vmh59S7EnKHwFaawmphUNbGoe2NsUbXh
This would result in a totally different wallet whose addresses wouldn't be "connected" at all with your previous ones even though you've "just" switched two words. The way that the "system" checks if your address is valid is by check sum - You can understand a bit more about the "math" behind it in this graph (taken from here[3]):
EDIT: If you're interesting in the checksum section, the previously linked website also has a tool[4] that let's you see that the public key for each private key shown before. Enter the private key on the field
Private ECDSA Key and the public key will appear right next to it - on the
Public ECDSA Key field.
As a closing remark we can - in a very simple matter - represent the process behind generating addresses like this:
Seed phrase -> Private Key -> Public Key -> Public Address
-> Represents derivation from the previous concept
Each time you "generate" a new address you're basically building a new private key and public key, which were themself "born" from your own and unique seed phrase.
[1]
https://www.blockplate.com/pages/bip-39-wordlist[2]
https://gobittest.appspot.com/Brainwallet[3]
https://bitcoin.stackexchange.com/questions/32353/how-do-i-check-the-checksum-of-a-bitcoin-address[4]
https://gobittest.appspot.com/Address