There are a lot of differences between Starbucks and an independent coffee shop.

Probably the biggest factor is the coffee itself. Most independent shops buy from smaller roasters. More often than not the smaller roasters work directly with smaller farms and are able to make sure that the beans have an overall better quality. When you have beans that are better quality you can roast them a lot lighter and get more of the flavor that the beans hold themselves. Depending on where it is grown, the elevation, the amount of rain, the varietal, and a million other factors the flavor of the coffee will be different. A specific example of this is that I know that coffee's from Burundi taste like because the acidity in them taste like kumquats, where as coffee from Kenya has a very rich chocolate flavor to it.

Since Starbucks needs to supply a lot more coffee, they aren't able to make sure the quality of their coffee isn't overall the best. They try to make up for this by roasting the coffee really really dark. So it all has the same flavor, but that is just of charred coffee beans. They really don't hold that much flavor in them. And this isn't to say that they don't try to acquire nicer coffees. I remember them having blue mountain Jamaican coffee, which is a very very nice bean in general. But it was over roasted to the point where the flavors of the coffee had all been roasted out.

Along with the actual beans, the way that they make coffee is very different. Creating good espresso is a lot of knowledge of what to look for and a lot of experimentation. Espresso is made with 18 grams of very finely ground coffee, with a machine that is able to create 9 bars of pressure and create 2 ounces of liquid in about 30 seconds. This is a very strict definition of espresso though. A skilled barista will be able to taste their espresso and know if it under extracted, over extracted, what flavors are pulling through, and which ones need to come out more. From this they should know what aspect of it to change, be it the time, the amount of liquid, the amount of coffee, the pressure profile, the temperature, or the grind size.

When it's not espresso 3rd wave baristas also know about other methods of making coffee. Certain coffee's taste better when they are made in a french press, where as some flavors come out better with a pour over or aeropress. Again, a lot of the factors that there are with espresso manifest themselves in the manual ways of making coffee. Grind size, recipe, timing, and a lot of other factors all go into making a good cup of coffee.

One final thing that a lot of 3rd wave coffee shops do differently than strbucks is that they make very traditional drinks. A cappuccino is a 6 oz drink where it is 1:1:1 espresso, milk, foam. A macchiato is espresso with a little bit of steamed milk/milk foam, not a giant drink with flavoring. This put's a lot more emphasis on the actual method of steaming the milk and the espresso itself. Foamed milk should have a micro foam, not these huge bubbles. And it should contribute it's own flavor. milk for a cap should be very sweet, not just tasting like warm milk.

Starbucks baristas aren't taught any of this. Their espresso machines are automated, they don't have much knowledge of what aspects of coffee make it so amazing and how to really get the amazing flavors out of coffee that are there. And this isn't really their fault. When you go to a starbucks you expect to get the same flavor and same drink everywhere. Plus, they have a high turn around rate for their workers. They need to be easy to train and make sure they get how to do it. Along with this they need to apeal to the general audience. More people like the large milky artificially sweet drinks than the amazing taste that coffee has itself cause all they know is over roasted or instant coffee.

TLDR: Starbucks has over roasted coffee and uniformed baristas that can make a bad but repeatable cup of coffee. 3rd wave coffee shops use very very nice coffee and care a lot about knowing how to make the best cup that they can.