There are two types of computer programming errors ...

Compile-Time
One type is a compile time error. If there is a syntax error in the code, the compiler will detect the error and the program won't even compile. At this point, the programmer is unable to form an executable that a user can run until the error is fixed. Forgetting a semi-colon at the end of a statement, for example, is a compile-time error. It's something the compiler can detect as an error.

Run-Time
The second type is a run-time error. Compilers aren't perfect and so can't catch all errors at compile time. This is especially true for logic errors such as infinite loops. For example, the actual syntax of the code looks okay. But when you follow the code's logic, the same piece of code keeps executing over and over again infinitely so that it loops. In such a case, compilers aren't really smart enough to catch all of these types of errors at compile-time. Therefore, the program compiles fine into an executable file. However, and unfortunately, when the end-user runs the program, the program (or even their whole computer) freezes up due to an infinite loop. Other types of run-time errors are when an incorrect value is computed, the wrong thing happens, etc. Basically, a run-time error is anything that goes wrong in a program. It's any error or problem with the program that slipped by the compiler's error checker.

The Maintenance-Time Error
The original author didn't comment, used crappy and inconsistent code style, and obfuscated because it made him/her feel clever. So now when the system needs updating, the new team of coders takes one look at the codebase and flees screaming into the night.

The Beer-Time Error
The program will probably compile, and will probably even do what you want it to do. However, you may have some difficulty in determining just what you were thinking, later on.

The Out-Of-Time Error
Procrastination leads to panic. Panic leads to all-nighters. All-nighters lead to lack of sleep. Lack of sleep leads to incomprehension. Incomprehension leads to failure to understand what's wrong with C statements like if(3 = a) { ... . Failure to understand what's wrong with C statements like if(3 = a) { ... leads to frustration. Frustration leads to anger. Anger leads to hatred.

And we all know that hatred leads to the Dark Side.

>There are two types of computer programming errors ...
It depends on the language and what you consider compile-time. Compilation usually consists of two distinct steps: compilation and linking. Both of those steps may have errors that are unique to the step. Therefore, I would say that there are three types of errors for compiled languages: compile-time, link-time, and run-time. Link-time and run-time errors are by far the most frustrating. For interpreted languages there's no such thing as compile-time, and all errors are run-time whether they're syntax errors or logical errors.