There are at least a couple things we might mean by "steady state". First, there's the kind when we say we should wait four to five half-lives after starting a medication before measuring serum levels. This is due to the additive effects of consecutive doses. Each dose is modeled as making a rapid contribution to serum levels that decreases over time. The rate of decrease is modeled by an exponential decay and quantified by the half-life parameter. For any individual dose, after four half-lives the contribution is down to 1/16 of the starting amount. After five half-lives the contribution is down to 1/32. At these times we can be fairly confident that serum levels in subsequent dosing cycles should not increase by more than a few percent.
The key distinction with this kind of steady state is that it refers to variations between different dosing cycles, not variations within the dosing cycles. Unless the dosing cycle is short compared to the half-life we can expect a decrease in levels over the course of the cycle. That's why we usually measure at trough, before the next dose. The point here is that in steady state the serum levels in any cycle look the same as in any subsequent cycle, but these cycles can consist of post-dose peaks and pre-dose troughs that may be quite different.
The other steady state we're talking about means a minimal fluctuation in medication levels over the course of each dosing cycle. In other words, the serum peaks and troughs are relatively close together. We can calculate a ripple constant as the ratio of trough over peak, which is exp( -ln(2) * cycle_length / half_life). For example, if someone is injecting testosterone cypionate once a week and the half-life is five days then the ratio is 0.38, which means that serum testosterone has declined by 62% over the week, a pretty large variation. In contrast, if he injects daily then the daily decline is only 13%. In practice I think the ripple at shorter intervals is even smaller than this model predicts.
