Different environment
Cron passes a minimal set of environment variables to your jobs. To see the difference, add a dummy job like this:
* * * * * env > /tmp/env.output
Wait for /tmp/env.output to be created, then remove the job again. Now compare the contents of /tmp/env.output with the output of env run in your regular terminal.
A common "gotcha" here is the PATH environment variable being different. Maybe your cron script uses the command somecommand found in /opt/someApp/bin, which you've added to PATH in /etc/environment? cron does not read that file, so runnning somecommand from your script will fail when run with cron, but work when run in a terminal.
To get around that, just set your own PATH variable at the top of the script. E.g.
#!/bin/bash
PATH=/opt/someApp/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
# rest of script follows
Some prefer to just use absolute paths to all the commands instead. I recommend against that. Consider what happens if you want to run your script on a different system, and on that system, the command is in /opt/someAppv2.2/bin instead. You'd have to go through the whole script replacing /opt/someApp/bin with /opt/someAppv2.2/bin instead of just doing a small edit on the first line of the script.
You can also set the PATH variable in the crontab file, which will apply to all cron jobs. E.g.
PATH=/opt/someApp/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
15 1 * * * backupscript --incremental /home /root