In general, r represents the per capita birth rate minus the per capita death rate for a population (r=bd). In this tutorial we call r the intrinsic rate of increase, and we distinguish between two types of r:  
WHAT IT MEANS IN EACH MODEL:  EXPLANATION:  

maximum intrinsic rate of increase 
exponential:  rmax=(bd) rmax is constant 
Birth (b) and death (d) rates are constant because the population is unlimited by resources. 
logistic:  rmax=(bd) rmax is constant 
rmax
is constant,
but it is adjusted to obtain the realized rate (see below). 

r: 
realized intrinsic rate of increase 
exponential:  r = rmax r is contant 
The realized is the same as the maximum rate of increase because the population is unlimited by resources. 
logistic:  r = rmax[1(N/K)] r changes with N 
The realized rate of increase, at any moment in time, is obtained by multiplying rmax by the densitydependent term, [1(N/K)]. This "adjustment" takes into account changes in b and d that happen as density changes. 
