When looking at examples for how to define and run ansible scripts, some examples use 'ansible' command to execute the scripts and some examples use 'ansible-playbook' command. But I have been unable to find the difference between them or guidelines regarding which one to use when.
What are the differences between the two commands?
Ansible scripts are called playbooks.
By definition
A playbook is a list of plays. A play is minimally a mapping between a set of hosts selected by a host specifier (usually chosen by groups but sometimes by hostname globs) and the tasks which run on those hosts to define the role that those systems will perform. There can be one or many plays in a playbook.
https://docs.ansible.com/ansible/latest/reference_appendices/glossary.html#term-plays
Then, you execute your playbooks with the command ansible-playbook, for example this command execute the playbook test.yml on all servers in your inventory file:
ansible-playbook test.yml -i inventory all
with ansible command you can execute just a tasks against your servers, for example this command execute a task with the module ping on all servers in your inventory file:
ansible -m ping -i inventory all
Then the difference is with ansible-playbook you can execute a playbook with a lot of tasks and with ansible you just can execute a task.
Welcome to ansible world. Red Hat offers an introductory course of ansible you can take it, It'll help you a lot.