Local SEO is usually in relation to a specific location within your own country. International SEO, however, typically refers to the various SEO tasks undertaken to get your website (or a subdomain) ranking in other countries.
For example, you might have your original website in the UK (in English), but have now decided to operate in Germany. This might require you to have a subdomain for use in Germany (and in German). You would need international SEO, rather than local SEO for this.
As such, you’ll need to undertake various SEO tasks to establish this and ensure that search engines don’t get confused by the different subdomains. In essence, this means you can have exactly the same site in a different language on another subdomain. However, in Germany, the German site would rank, and in the UK the English site would rank.
Likewise, different countries respond to content differently, therefore your content will need to be tailored to each market. This includes conducting new keyword research, rewriting or optimising content using localised and region-specific terminology. You may also need to translate it into the relevant language.