Is it OK to use different variables inside the conditions of an if-else block

Consider that you have 2 different variables A and B. I have come up with the following case:

if (condition about A) {
  // do something...
} else if (condition about B) {
  // do something...
}

Is it OK to start the if statement by checking variable A and then continue with the else if by mentioning B? Doesn't this action change the context that was initially set when writing the first contition?

I would expect to see code like this:

if (condition1 about A) {
  // do something...
} else if (condition2 about A) {
  // do something...
} else ...

• or something similar about B,
• or something similar about both A and B with the use of &&, ||.

My example comes from one of the Codeschool js courses and I found it a bit confusing. Is it OK to write if statements like this?