Yes, in Chinese 紧张 means both.
"Nervous" means that you are feeling anxious or apprehensive about something that is going to happen or about to happen.
For example: "I am nervous about getting my blood drawn." or "I am nervous about passing my English test."
"Tense" is a feeling that happens when you are nervous or stressed.
For example: "Getting my blood drawn makes me tense." or "I'm just tense about my English class."
"Tense" is less severe and less emotional than "nervous", so "tense" is more appropriate in a business setting or when you are self conscious about how you might come across.
"Tense" can also refer to stressed and have nothing to do with nervousness.
For example: "With all the work he has to do, he seems very tense." or "I get really tense when I have to do too may things at once."
The word "tense" comes from people tensing up or clenching their muscles when they feel scared, anxious, nervous, or stressed, so it doesn't have as specific of a meaning as "nervous".
I hope this helps!