I set up a test server on Ubuntu locally at the office, and when I installed mysql and I ran the mysql -V command, I get this result:
mysql Ver 8.0.19-0ubuntu0.19.10.3 for Linux on x86_64 ((Ubuntu))

And on the DigitalOcean droplet, the result is one:
mysql Ver 8.0.19 for Linux on x86_64 (MySQL Community Server - GPL)

1. What’s the difference between the two installations?
2. Why they have different my.cnf configurations?

my.cnf for mysql Ver 8.0.19-0ubuntu0.19.10.3 for Linux on x86_64 ((Ubuntu)):

[mysqld]
#
# * Basic Settings
#
user        = mysql
# pid-file  = /var/run/mysqld/mysqld.pid
# socket    = /var/run/mysqld/mysqld.sock
# port      = 3306
# datadir   = /var/lib/mysql


# If MySQL is running as a replication slave, this should be
# changed. Ref https://dev.mysql.com/doc/refman/8.0/en/server-system-variables.html#sysvar_tmpdir
# tmpdir        = /tmp
#
# Instead of skip-networking the default is now to listen only on
# localhost which is more compatible and is not less secure.
bind-address        = 127.0.0.1
#
# * Fine Tuning
#
key_buffer_size     = 16M
# max_allowed_packet    = 64M
# thread_stack      = 256K

# thread_cache_size       = -1

# This replaces the startup script and checks MyISAM tables if needed
# the first time they are touched
myisam-recover-options  = BACKUP

# max_connections        = 151

# table_open_cache       = 4000

#
# * Logging and Replication
#
# Both location gets rotated by the cronjob.
#
# Log all queries
# Be aware that this log type is a performance killer.
# general_log_file        = /var/log/mysql/query.log
# general_log             = 1
#
# Error log - should be very few entries.
#
log_error = /var/log/mysql/error.log
#
# Here you can see queries with especially long duration
# slow_query_log        = 1
# slow_query_log_file   = /var/log/mysql/mysql-slow.log
# long_query_time = 2
# log-queries-not-using-indexes
#
# The following can be used as easy to replay backup logs or for replication.
# note: if you are setting up a replication slave, see README.Debian about
#       other settings you may need to change.
# server-id     = 1
# log_bin           = /var/log/mysql/mysql-bin.log
# binlog_expire_logs_seconds    = 2592000
max_binlog_size   = 100M
# binlog_do_db      = include_database_name
# binlog_ignore_db  = include_database_name

my.cnf for mysql Ver 8.0.19 for Linux on x86_64 (MySQL Community Server - GPL) DigitalOcean:

[mysqld]
pid-file    = /var/run/mysqld/mysqld.pid
socket      = /var/run/mysqld/mysqld.sock
datadir     = /var/lib/mysql
log-error   = /var/log/mysql/error.log