According to the American Concrete Institute, the minimum compression strength for high-strength, high-performance concrete is 55 MPa. The reasoning is that to generate concrete with compressive strengths of 55 MPa or higher, special care is required for production and testing of the concrete. Please see the following web page
Yes, concrete that has 60 MPa compressive strength considered as high strength concrete according to ACI-2011).
ACI- Committee 363 defined HSC in 2011 as, a concrete that has a specified compressive strength of (55 MPa) or greater. (ACI Committee 363 2R-11, “Guide to Quality Control and Assurance of High-Strength Concrete”, American Concrete Institute, 2011.).
* The strength of concrete has to be correlated to a concrete grade defining a fractile (generally 5% for the lowest values)
* The results of compressive strength are not the same according to the type of specimen used (cylinders ou cubes)
For example : a concrete grade C50/60 in Europe means a 5% fractile value of 50 MPa on 15x30 cm cylinders and 60 MPa on 15x15cm cubes. That means the average value during concrete production is higher.
During the concrete design stage in laboratory, we usually consider the compressive strength values should be > 1,2 * fractile value because the concrete batches in lab are well controlled
In my opinion, attention should also be paid to the test method (sample type). The requirements for cylindrical samples h/d=2 are lower than for cubes 15cm or 10cm. Comparing the results obtained on 10cm cubes with the requirements of eg USA for cylindrical samples is not correct.
The important thing is what Maxime Lion wrote: "compressive strength values should be> 1.2 * fractile value" 20% more when designing concrete in the laboratory is a big difference and not everyone pays attention to it.
It is obvious that there are other requirements for high performance concrete. In my opinion, ensuring proper consistency and workability after 60 and even 90 minutes is as important as durability.
According to EN 206 the high strength ordinary concrete is the one of class C50/60 which means that compressive strength determined on cubes of size 15 cm must be at least 60 MPa (while determined on cylinders of height 30 cm and diameter 15 cm must be at least 50 MPa), but this numbers concern characteristic value (fck), not the mean value (fcm).
So the question is, which strength value are you asking about?
If you consider results obtained on the way of testing the specimens, you need to take into consideration the statistics (the average value, the minimal value) before comparing the results to the characteristic value of 50 or 60 MPa and classifying the concrete.