What has changed is:
Rapid fire now activates instantly instead of after her first attack.
Rocket jump does not cancel in midair when CCed.
Explosive shot is now an auto attack reset, it's duration has been lowered however can be increased by auto attacking the target. Explosive shot's passive is not in effect during its cooldown.
Buster shot's range now scales with Tristana's level.
Rapid fire not activating immediately was always a bug which was never fixed. A QOL change.
Rocket jump is somewhat of a lackluster escape tool, it not only has a channel time before she takes off, if she is hit by a stun or snare in midair she drops to the ground where it happened. This change is to make it less of a comic relief of escape tools.
When playing Tristana late game there is no reason to ever be that close to use her E on a target, now it scales with her passive as it is an autoattack augment. Also her passive explosion can make it hard to last hit and pushes the lane, now it is semi-togglable letting you turn it off by using the skill.
Also it gives more of a use for her passive and her Q while playing AP.
Like the above, there is no reason to be that close to an enemy to use buster shot. It now scales with her passive as well. At level 6 it will have 695 range.