What is the difference between these 2 chain tools?
 

chain plier and chain breaker

It depends. Currently, a “chain plier” is a tool used to remove or install a quick link and is more correctly called a master link plier. A “chain breaker” is used to push the pin from a chain link.

Long ago, there were chain pliers made to push the pins from a chain link. They never really worked that well because the force required to remove a pin is considerable. The Park chain pliers were a little easier to use than then ones like this design

One can readily "get by" without having a chain plier. There are work-arounds.

One can barely "get by" without a chain breaker.

Now, if you're willing to have a bike shop do all maintenance for you, then you don't need either. But if you intend on maintaining your own bike, changing or cleaning worn chains, shortening new ones to fit and the like, you need both. The last thing is a small piece of heavy gauge wire twisted into a "C", or sold like this:
https://cimg4.ibsrv.net/gimg/bikefor...9d37aae86.jpeg

^ super convenient to relieve chain tension when your shortening or re-joining chains.

I beg to differ. The Gian Robert chain pliers I bought for the charity shop where I volunteer has become the preferred chain tool at the shop. The various Park screw-type tools go neglected much of the time. The biggest problem with the chain pliers is not the force needed to push the pin, but the profusion of chain widths, some of which require a deft touch to prevent the pin from being pushed too far.

The Park CT-2 is nice in that the stroke of the tool can be adjusted to accommodate different chain widths in a manner that isn't easily possible with other chain pliers. But making that adjustment requires a degree of attention that is not always present in many mechanics. I've used the VAR-303, which is quite similar to the Gian Robert pliers, but is less accommodating to a variety of chain styles. I sold the shop's VAR-303 to purchase the Gian Robert pliers.

An old spoke is the ideal source of a "heavy gauge wire" from which to fabricate this tool.

I used an old brake spring

A wire clothes hanger is easy to cut and bend too.