Is having sensitive teeth the same thing as having weak teeth?

Not necessaily: Sensitive teeth is usually caused by gum recession or root exposure of the tooth. This has nothing to do with the strength of a tooth.

Not necessarily: There are a few rare conditions that actually make teeth weak if they don't form properly. Most people that say they have weak teeth mean that they get cavities easily - usually from poor hygiene and diet. Teeth can be sensitive for many reasons, one of which would be having cavities, but there are many others. If your teeth are sensitive, see your dentist to find the cause and treat it.