Clearly, there is no standard rules on how you should categorize your automation, it all depends on your project size, schedule and product complexity.
ASAIK, in general, testers usually break down their automation based on their needed and the resources available.
Here is a brief ideas on different type of tests (It vary depends on the complexity of the product)
When to run?
How long to run?
What covered?
Purpose
Run Contexts
Build Verification Tests (BVT)
After each build
50% build time
Pri 0 issues
Sanity check for build quality
Default
Unit Tests
Before check in
5 -30 minutes
API level functionalities
Prevent new check-in causing regression
Buddy Tests
4-8 hours
Areas around the check in
Ensure the quality of the check-in
Manual
(Random)
Nightly Tests
Every night
< 24 hours
Pri 0 - 1 issues
Keep product quality in known state
Rotate
Weekly Tests
Every week
< 3 days
Pri 0 - 3 issues
Full Suite Tests
Each Sign off/
milestone
2-4 weeks
on all contexts
Sign off/Verification
All
Code Coverage Tests
Each major milestone
Found out what had not been covered
Identify missing coverage and fill it
User Scenario
Feature complete
1-2 hours each
User scenario of individual feature
Ensure feature complete meet customer expectation
(random)
Demo Scenario
Each major milestones
4-8 hours each
User scenario across multiple features
Prevent cross feature integration issues
End to End Scenario
When product is dogfood-able
1-2 weeks
User scenario from End to End
Ensure best End to End user experience