I was about to post and just noticed Sensei Goldsbury has beaten me to it, so I'm not adding much now but since I wrote it anyway…
From my own experience the difference in usage is more a nuance of feeling.
- Keiko 稽古 has the feeling of practising a discipline for oneself. Imagine a good dojo with a good teacher and plenty of good students: If you don't turn up for keiko it is mainly you who is missing out. Everyone else just misses one student. If you call this practice renshuu, it's fine but not as nuanced.
- Renshuu 練習 has more of a general feeling of practice as well as the feeling of practising for or with others. For example, aikido, practise for a demonstration would be called "renshuu". I've never heard it called keiko in this kind of situation, especially outside of martial arts or other disciplines. The baseball team usually has renshuu, not keiko.