Yes, standard kitchen counters are 36" off the floor, but depending on countertop thickness and standard cabinet heights, this overall height can vary from 35 1/2" to 37"
Bar height is 39"- 42", as shown on the bar in this picture.

Rebekah is correct, but if it is custom you can do as you please.

How about upper cabinets?

More often than not the bottom of the upper cabinet is 18" above the countertop. Height depends on ceiling height and your comfort with high access.

Be warned, our counters are not a standard height and when we went to purchase a new stove we had big problems.

we always have it 2-3 inches less than the end users elbow height.. not all clients are of the same height to have a standard 36" high counter...

Miele says you need a min. counter height of 38 3/4" to install their 6000 series oven and induction cooktop due to a 6" toe needed so the oven door doesn't hit the floor when opened. This seems very high. Any thoughts?

PO used elbow height on their bar counter. He was tall. As a result, bar stools made people feel like little kids. No one sits there, so we stashed the stools and just use it as a pass through. upcoming remodel says bye-bye to out of standard counter height.

It's not a good idea to go outside of the standard counter heights - there are always problems. If I have short or tall client who wants a 'comfort height', we either drop/raise a section or make sure none of the appliances are in the island and do the height adjustment there.

is the height of kitchen island and kitchen counter the same?

That is correct.

Related question: I have a new kitchen that is going to be installed. Base cabinets are standard 34.5". I am getting 3 cm granite with a 3 cm laminated edge for a 6 cm look. Questions: 1. how high will my countertop be with this laminated edge? 2. I have an island with one a dishwasher and sink and the free standing range is on the counter by the wall. Should we NOT shime the cabinets by the wall and then install the 1/2" floor tile to help offset the counter height and allow the stove to better fit? 3. And then I assume we must shime the Island base cabinets a 1/2" or the washer will not fit, correct? Desperate for advise as now one seems to have a clear answer on this issue with the thicker counters.

@stolenbuick, May I ask if you hired an architect, interior designer, or is this DIY? Questions such as this are my worst fear in our upcoming remodel so I chose to go with an architect.

With 34 inches counter height at what height should you purchase barstools?

@Andrea - have a look at this site... might be helpful. https://www.improvementscatalog.com/RoomForImprovements/how-to-choose-the-right-bar-stool-height/ 

What is the depth of the counter and worktop on this photo?

The stone counter is 2'-1" and the wooden counter above is 2'-0" and overhangs the lower stone by one inch.

And what is the depth of worktops on other units (hob and the one to the right)? Is it 2'1" as well?