|| is the logical OR operator. It sounds like you basically know what that is. It's used in conditional statements such as if, while, etc.
condition1 || condition2
Evaluates to true if either condition1 OR condition2 is true.
| is the bitwise OR operator. It's used to operate on two numbers. You look at each bit of each number individually and, if one of the bits is 1 in at least one of the numbers, then the resulting bit will be 1 also. Here are a few examples:
A = 01010101
B = 10101010
A | B = 11111111
A = 00000001
B = 00010000
A | B = 00010001
A = 10001011
B = 00101100
A | B = 10101111
Hopefully that makes sense.
So to answer the last two questions, I wouldn't say there are any caveats besides "know the difference between the two operators." They're not interchangeable because they do two completely different things.