Because 'get' can mean many things! On its own, 'get' has three main meanings:
- to arrive/to reach
- to take/obtain
- to become
Your two sentences are examples of the first two. 'He got ill' is an example of the third.
'Get' can also combine with other little words to mean hundreds of different things - get off, get out, get up, get though and many more.
It's a hardworking little word!