Tor is not a browser. It is an proxy software. your browser uses that software.
Google "how proxies work" or "proxy"
basically you use another remote computer to browse all the web sites. So it that proxy web site that gives you web site data and you only browse that proxy web site. It does your work, you browse thorugh it so all the web sites sees the proxy server and not your PC.
There is no true way to be anonymous. In a top/ip session there is always a source and destination IP. While the destination may see the proxy or VPN service instead of your ip, the service you are using has a record of which ip initiated the connection. So in summary, you have to trust that the proxy or VPN service protects your identity.