A couple of years ago I bought a cheap tile saw for some tile work.  I ended up not using it for a couple of reasons. 

First, score and snap cutting is much faster.

Second, the saw would cause chipping on the glazed surface that was unsightly.  Instead I cut with a good scoring cutter and use a carborundum stone to make the glazed surface perfectly smooth and straight.

But the other day I watched an online video where they used the identical saw as I have and they were ending up with very clean cut edges.

Will a different blade resolve this issue?  I’ve only cut about 5 or 6 tiles with the factory blade.  If I do buy a new blade, what should I look for?

It is a Skil 7” wet saw.

All about the blade and feed rate. I have someone else's version of that saw I use for small work. Have a big 10" on a stand for larger work. With that el cheapo small saw you really have to pay attention to straight feed. The factory blades on those will easily flex if you don't feed straight resulting in chipping. Factory blade is good for cuts that will be hidden behind something, i.e. a corner, another tile edge etc.
I've bought Home Depot MK blades, blades from briggs & brackston, https://www.bbindustriesllc.com, etc. You have to spend money a good blades, whether its tile or wood working.
Different tile, different blades. Oddly some of the cheap blades I've bought at Menards worked out really well.

So, is the consensus that a better blade could minimize or eliminate the chipping?

The other issue I have with this is sometimes at the end of a cut the two pieces break apart leaving one corner with a major chip.

To some extent I minimized this issue by using a piece of plywood to push both sides of stock at exactly the same rate, but none of the videos I’ve seen address that issue.

Yes & no. It will be dependent upon the amount of runout that the Skil saw has. If there's little runout then the chance is greater that a better blade will cure your ills. If there's a lot of runout in the Skil, then not so much.  It seems blades are getting better every 3-4 years.

I have used blue painters tape to cover the cut line and that does help somewhat, but again...depending upon the blade.

These were cut with an ATS dry blade in a TSC 55. The 2nd photo using NO tape, the 3rd photo using painters tape. In my evaluation the cut went from terrible to usable if placed in the right position.







Like Holzhacker mentioned, one of the best sources I've found for dry or wet blades is Braxton Bragg now known as BB Industries.

We used large format porcelain tiles in our bathroom. My wife even wanted the walls tiled 1/2 way up. I have a small wet tile saw and a large 10" wet saw from Ridgid (ha, called the BEAST). To get decent cuts I ended up purchasing a Montolit 63P3 tile cutter. I was planning on selling it after the job but it worked so well I ended up keeping it. That was in 2018 and I purchased it direct from Italy.

For the cut edges, I found a CBN sharpening card worked the best to slightly chamfer the edges.

Edit - forgot to mention, you can use a snap cutter where you are working so ne need to run in/out of the house.

Speaking of CBN, like diamonds saws CBN grinding wheels have to run true. There is no possibility of truing them by dressing. So the shaft has to be straight and the washers have to be flat.

Check the condition of the washers. For CBN wheels they sell thick flat washers.