Chain Splitter vs. Chain Tool vs. Chain Breaker
Most likely the same.

I think there are only really two "chain" tools (i.e. tools with "chain" in their name). One is used to break a chain, and goes by names such as chain splitter or chain breaker. So you'd use this for removing a chain completely off the bike, for example to replace it. You might also want to look at Power Links in this context, as using a Power Link means you can sometimes avoid using a chain splitter altogether (which requires a degree of precision).



The other is used to hold a freewheel/cassette in place, and is called a chain whip. You'd typically use this in conjunction with a lockring, when you want to remove the freewheel/cassette.



Unfortunately I've heard both called a "chain tool".