LTM load balances servers as well as does caching , compression, persistence, many more. GTM load-balances data centers.
In a normal deployment, a customer will have two data centers, each with GTM and LTM devices. For GTM to work efficiently, customers delegate DNS resolution to GTM.
So, a user might just type into their browser “www .example .com .” GTM will see the DNS request and see which data center was performing best. If it was data center 1, GTM would return the IP address from the LTM in data center 1. Then, the user will connect to that IP and also LTM would load balance the user’s request to a server.