either or 包不包括两者

"Either A or B" most precisely means, in symbolic logic terms, "A XOR B", where XOR is the "exclusive or". So yes, it means "A or B but not both". It isn't always actually used with full precision, though, so, as usual, context has to be taken into account. If somebody says, "select either A or B", for example, they definitely mean that you should not select both. If they say "if either A or B is true", though, they probably mean a non-exclusive OR, and the condition is still true if both A and B are true. Unfortunately, if there's a generally reliable rule for telling which is meant, I'm failing to think of what it would be.

Without the "either", the presumption would be more toward "A OR B", where OR allows the case where both are true. Which is why computer geeks and propositional calculus nerds will, when asked "do you want to go to lunch now or later?", answer "yes". (Illustrating that the "either" part is implied by context as often as it's cancelled by context.)

也就是说逻辑中 either...or...表示 XOR，日常使用看语境。