Differences between Time Tracker / Time Tracker Lite

For Jira Server:

Time Tracker offers 3 reports and 4 gadgets:

Time Sheet Report and Gadget—provides details to analyze workloads by displaying summaries of worked hours in Jira.
Project Pivot Report and Gadget—displays summary of worked hours in a project of a certain period.
Timespent Report and Gadget—displays the total time spent per issue in a single-column table.
Worked Time Chart Gadget—visualize time spent on issues in a pie chart.

It also offers two features that Time Reports does not:

Time Tracker Lite offers 13 reports and 1 gadget that allows users to display 12 reports:

Reports with gadget support:

Time Entry—single day view.
Timesheet—time spent on issues by days.
Calendar—summary of worked hours per day in a calendar view.
Timespent—single column table.
Pivot by User—time spent on issues by users.
Pivot by Status—time spent on issues by status.
Pivot by Label—summary of worked hours spread over columns from worklog comments.
Time Tracking—estimated vs actual.
Pie Chart—time spent chart.
Time In Status—time passed in status.
Resolution Time—time passed until resolution.
Time Balance—changes in time tracking fields over time.

Report only:

Cost Report—the cost for a certain period, based on hourly rates [NO GADGET SUPPORT]

For Jira Cloud:

Time Tracker and Time Tracker Lite offer the same 13 reports and 1 gadget that supports all 13 reports:

Time Entry—single day view.
Timesheet—time spent on issues by days.
Calendar—summary of worked hours per day in a calendar view.
Timespent—single column table.
Pivot by User—time spent on issues by users.
Pivot by Status—time spent on issues by status.
Pivot by Label—summary of worked hours spread over columns from worklog comments.
Time Tracking—estimated vs actual.
Pie Chart—time spent chart.
Time In Status—time passed in status.
Resolution Time—time passed until resolution.
Time Balance—changes in time tracking fields over time.
Cost Report—the cost for a certain period, based on hourly rates.

The main differences lie in the additional features that Timesheet Reports and Gadgets offers:

Log work for other users: on Time Tracker you can select specific groups to be able to log time impersonating other users
Email subscription: this feature allows you to send a email or create a email subscription for the reports that you wish, see this documentation Email Time Sheet Report for more information;
REST API integration: You can use REST API integrations in Timesheet Reports & Gadgets for Jira Cloud
Some degree of work logging automation: see Log Suggested Work Automatically