The study of life outside of our own biosphere can be divided into three categories:

1. Life not native to Earth. I would call this "exobiology". We haven't discovered it yet, so it is entirely theoretical and shouldn't (yet) have a tag.

2. Life native to Earth, surviving in an environment not like Earth. Tardigrades, bacteria, and other species studied in the vacuum of space would all be examples.

3. Life native to Earth, surviving in an Earth-like environment. This is just simply regular life-support, or terraforming.

The reason we study #2 in the first place is that is gives us many clues about the possibility of #1. Also, should #1 even exist, the chances are far greater that it is in a non-Earth-like environment than an Earth-like environment. Therefore, I would define astrobiology as

The existence or survival of life in an environment that is not like Earth.

The study of life outside of our own biosphere can be divided into three categories:

1. Life not native to Earth. I would call this "exobiology". We haven't discovered it yet, so it is entirely theoretical and shouldn't (yet) have a tag.

2. Life native to Earth, surviving in an environment not like Earth. Tardigrades, bacteria, and other species studied in the vacuum of space would all be examples.

3. Life native to Earth, surviving in an Earth-like environment. This is just simply regular life-support, or terraforming.

The reason we study #2 in the first place is that is gives us many clues about the possibility of #1. Also, should #1 even exist, the chances are far greater that it is in a non-Earth-like environment than an Earth-like environment. Therefore, I would define astrobiology as

The existence or survival of life in an environment that is not like Earth.

which would cover #1 and #2.