Difference between Clock and date in F5

Very confused about what you're asking here - all of those things are taken from the system clock which is controlled by NTP normally or if not then can be set using the date command.

AFAIK, the dates should match whether you are using the

tmsh show sys clock

date

clock

The LTM logs should reflect the time zone too.

Do you have a timezone configured?

tmsh list sys ntp timezone

The output should be something like this

sys ntp {
    timezone US/Eastern
}