ansible: difference between a variable and a fact

While I'm using Ansible for quite some time, I'm not sure I really understand the differences between a variable and a fact.

Would it be any difference doing
- set_fact:
nginx_ssl: /etc/nginx/ssl
nginx_conf_file: /etc/nginx/nginx.conf


or
vars:
nginx_ssl: /etc/nginx/ssl
nginx_conf_file: /etc/nginx/nginx.conf


Could someone explain me, possibly with an example where it really make a difference ?

Ansible facts are data collected about the (target) systems on which Ansible takes actions. They are variables, but set by Ansible (in a way like system defined variables). They are collected during Gathering Facts stage of a playbook run, and it is controlled by the gather_facts setting. Ansible calls this variables discovered from systems. That said, it is possible to set custom facts also.

Some examples are:

• ansible_hostname - the FQDN of the target system

• ansible_os_family - the Operating System family of target system (RedHat, Debian, etc.)

The other variables are the ones we can set as per our requirement (in a way like user defined variables).

Some examples are:

• my_fav_fruits: [ 'orange', 'apple', 'banana' ] - yours might differ.

• config_dir: '/etc/my_app/conf.d' - for my application configuration files.

Update:

Updating answer to make it relevant to the edit(s) made in question.

As @Bruce Becker's answer rightly pointed out, there is a difference in the precedence of variables set with set_fact. Also variables that need to be set at "run time" can be set this way. Without further explanation, taking your example variables, if I create a play like below:
- hosts: localhost
vars:
nginx_ssl: '/etc/nginx/ssl'
nginx_conf_file: '/etc/nginx/nginx.conf'

tasks:
- name: set nginx path to /opt when running on Debian
set_fact:
nginx_ssl: '/opt/nginx/ssl'
nginx_conf_file: '/opt/nginx/nginx.conf'
when: ansible_distribution == 'Debian'
- debug:
msg: 'ssl: {{ nginx_ssl }} and conf: {{ nginx_conf_file }}'


Then the set_fact variables will take precedence (on Debian) and output will be:

"msg": "ssl: /opt/nginx/ssl and conf: /opt/nginx/nginx.conf"

On other distributions, it will be what was declared in vars:.

StackExchange DevOps Q#12386, answer score: 6