Three levels of rules
Shorthand checks, in order, and uses the first rule that applies:

A snippet set to “Same as group” follows its group; a group set to “Default (from Preferences)” follows Settings.
The default for all groups
Open Settings ▸ Expansion.
In Expand snippet groups in, choose All applications, All applications except… or Only these applications….
For the last two, click Add Application… and pick apps. Remove one with its minus button.
Example: exclude your code editor so abbreviations never fire while you program.
A whole group
Select the group in the sidebar.
Under Expansion, set Expand in to one of: Default (from Preferences), All Applications, All Applications, Except…, Only These Applications… or No Applications (Disabled).
Add apps with Add Application… if needed.
Example: a group of terminal commands set to Only These Applications… with Terminal.
A single snippet
Select the snippet.
Set Expand in: to Same as group, All Applications, All Applications, Except…, Only These Applications… or No Applications.
Add apps with Add Application….
Same abbreviation, different apps
When more than one snippet has the same abbreviation, the one aimed at the current app wins: a snippet set to “Only These Applications…” beats one set to “All Applications, Except…,” which beats a general one. Snippet rules count before group rules.
Example: two snippets with the abbreviation ;sig:
Snippet
Expand in:
Result
“Best, John” (casual)
Same as group (all apps)
Used everywhere else
“Kind regards, John Appleseed, Example Ltd.” (formal)
Only These Applications… Mail
Used in Mail
Snippet suggestions follow the default in Settings ▸ Expansion ▸ Expand snippet groups in: phrases typed in excluded apps are never counted.
Snippets still don’t expand in an app you allowed? See Troubleshooting.
Related: Groups · Abbreviations & Expansion
