Some performance measurement tools add instrumentation to the code. E.g. they may binary translate, and add instructions to read the timers at the beginning and end of functions. Or this instrumentation, this reading of the timers, may be added to assembly, or C code, by an automated tool, or a programmer.
Other performance measurement tools do not change the code that is being measured. E.g. UNIX prof sampling runs special code that is invoked at the timer interrupt, which generates a histogram of the instruction at which the interrupt is received.
Some tools are hybrid: e.g. UNIX gprof combines prof-style interrupt sampling with mcount instrumentation added by the compiler -pg option to count which functions call each other.
All performance measurement has overhead, but instrumentation tends to have more overhead than interrupt based sampling. On the other hand, instrumentation can measure more stuff.