Yeah. It's part of the greater boston area and is across the river from the boston borders. In the cities that's close enough to be wrapped up as part of the bigger city.

No, Cambridge isn't Boston.

Cambridge is very close to Boston, but it's a different city. They're on opposite sides of the Charles river. These days the river is very narrow (it used to be a lot wider in colonial times, but they've drained swamps and built over them since then). The two cities have integrated mass transit systems, and it's a short walk across one of the many bridges to go between the two.

But, they're not the same city. The two places have different characters. Boston has "Southie", the Red Sox, the Celtics, the Bruins. Cambridge is much smaller and has MIT and Harvard. It has no sports teams (other than the school teams) and is a very rich and diverse city because of those rich and diverse schools. Politically it is very different from Boston. People jokingly call it the People's Republic of Cambridge because even by Massachusetts standards it is very left leaning.

Cambridge borders Boston, and is basically surrounded on 3 sides by Boston. Harvard is about 5 km from Boston's downtown, and MIT is about 3 km.