No, with a 10" table saw, you only use 10" blades. The difference is in the number off teeth and the job you are doing. 10" miter saws have a certain arbor size, as does 12" miter saws. They are different and cannot be interchanged. All 10" blades are the same whether they are for a table saw or miter saw. The more teeth you have the finer the cut (and the more expensive the blade), while a 40 tooth blade is fine for normal everyday cutting, you may have the experience of cutting wood that will tend to splinter. Then you change to an 80 tooth blade, or more.
If you get into blades, you can start with the basic Diablo or Dewalt blades. They are not as expensive as others and will serve for the interim.

I have about 25 or 30 blades, both in 10 and 12" sizes that I keep sharpened. I have a local guy do the work. Charges about 25 cents per tooth. Not free, but better than buying a new blade every time one gets dull. He gets them so sharp, he rolls them in hot wax to protect the tips and so I don't cut myself when transporting them.

 

Chandler, so a 7 - 1/4 handheld circular saw will only take 7-1/4 blades? Cannot take smaller? Do they make 7-1/4 dado blades?

I was dismissing circular saws fearing them to be cumbersome and heavy, but this Dewalt lightweight one has me considering it. And then table saw in the future as I learn more.
Amazon.com: DeWalt DWE575SB 7-1/4-Inch Lightweight Circular Saw with Electric Brake: Home Improvement

 

Why would you want to use a smaller blade? Yes, you should only use the size of blade called for by the tool. If you need smaller blades, then a smaller saw is called for. With all that said, you CAN install smaller blades on circle saws, but, again, why?

Dado blades won't fit on a circle saw. Too wide. Too cumbersome. They are probably relegated to use on radial arm saws and table saws only. Never seen one you could use elsewhere.

The Dewalt is a good saw. I like left handed saws myself. I just don't understand the logic of having to look over the tool to see where my blade is. I look down and can see my blade on the left side of the motor. Only available in certain brands, however. Mine is Porter Cable.

 

Chandler, I don't know why. LOL!

Just trying to learn about this world. Covering my grounds, and getting the stupid questions out of the way. Well, I'm sure I have many more dumb questions. I just got through buying and understanding a drill press, and I guess my curiosity comes from that. With 1/2 chuck, I know my press will take bits with shanks up to 1/2. So I'm just wondering how do you shop for blades.

 

Forrest is probably the "best", but they cost around $100 each. You can do fine work with a $39 blade. Look at HD or Lowe's for a selection and note the differences.

 

It's not always about being careful. Things can and do go wrong unexpectedly. I don't use my SawStop any differently than I use any saw. Always with caution.

The most common size arbor for 10" saws will be 5/8". I don't think you are going to find variation with this when shopping locally for "American" brand tools. There is a bit more to cut quality than just the number of teeth. There are different type of grinds for the teeth and their angle to the centerline of the blade affects the way they cut. For most work, the blades you get at the local hardware store will do you just fine. When you get into cutting veneered plywoods and especially melamine, you will want to find a more specialized blade.

I don't know if Forrest is the best, but they do make great blades and are the brand I buy for my home shop. Mainly because I have used them before and know they perform well. I don't want to risk buying something else and not having it do what I need it to do. By the way, they are north of $100 per 10" blade these days. The Forrest Dado King is an EXCELLENT dado blade. The best I have ever used.

Even in a professional shop, carbide blades will last several years with sharpenings.

 

Set the blade height for one inch. Set the fence one inch from the opposite side(outside) of the blade. Turn the 2x4 on its edge and do a cross cut using the mitre slide. This makes a one inch deep cross cut as if you had used a hand saw with the hand saw blade held vertically.

This next part requires a jig to hold the 2x4 vertically to make the second cut which would be like a rip cut but with the work piece held vertically and cutting in one inch from the end. Holding the piece vertically and passing through the saw gives a clean corner cut. THIS WILL ONLY WORK FOR SHORT STOCK. DO NOT TRY THIS STEP WITH LONG BOARDS.

Others will clarify if this is not clear.

 

Be sure to use a jig to cut the 2x4 on its end. This is a dangerous cut to make without one. Especially for a novice.

 

Want to borrow my Multimaster???? I'd never make a cut like this without my Delta tenoning jig, no matter how long the board is.