The language physicists use in describing this is the following: “The electron can turn into a virtual photon and a virtual electron, which then turn back into a real electron.” And they draw a Feynman diagram that looks like Figure 4. But what they really mean is what I have just described in the previous paragraph. The Feynman diagram is actually a calculational tool, not a picture of the physical phenomenon; if you want to calculate how big this effect is, you take that diagram , translate it into a mathematical expression according to Feynman’s rules, set to work for a little while with some paper and pen, and soon obtain the answer.

The emphasized part of this paragraph is such a good point. The way we talk about Feynman diagrams makes many students and working physicists think of them as representations of the actual physical process that is happening in QFT. In reality they are just graphical tools for representing the calculation of a power series (either formal or asymptotic).