If you want to backup a website hosted at HostGator, for example, to upload it to your hosting plan at Hostinger, follow these steps:
Log in to your Bluehost control panel
Navigate to Advanced → File Manager
Click on the Site Backup and Restore menu
Navigate to the public_html folder of your domain, select the files, right-click, and select Compress
Now you can then download the backup by right-clicking on it and selecting Download
Additional Resources
You can check the guide from Bluehost here: How to Create a Manual Backup of Your Website
If you need further help, make sure to contact Bluehost support