Semi-acoustic guitars are also known as hollow-body electric guitars, and both are types of semi-acoustic guitars. Semi-hollow body (or chambered) guitars are made from a single block of wood with a small cavity for resonance. In contrast, like acoustic guitars, fully-hollow body guitars are made from sheets of wood. The former has a depth similar to that of an electric guitar, whereas the latter may be deeper.
When a fully-hollow body guitar has an arched top, it is called an archtop guitar. Gibson Super 400 CES is a famous example of an archtop guitar.
Semi-hollow body guitars are heavier and have fewer feedback issues but produce less volume when played unplugged. In contrast, fully-hollow body guitars may produce a sound on par with an acoustic-electric guitar. This seemingly adds further complications to making a choice. Still, generally, unless you have a specific reason to choose a fully-hollow body or an archtop guitar, you can safely opt for a semi-hollow body guitar.
Semi-hollow body guitars are generally referred to as semi-acoustic guitars, and both terms are usually interchangeable unless specifically mentioned.