Yes, there are a couple key differences when you link two issues vs. connecting a pull request to an issue.
When you link two issues together, they will remain in the column where the "parent" issue is in. Even though you will use GitHub's Closing Language or Waffle's Connect Keywords to connect two issues, one issue can't close another or move it to a different column. If you connect a PR to an issue, you can choose to have the issue close automatically when merged. (More info on this here)
Two issues connected together:
A pull request connected to an issue: