There's a difference. In the "hygiene hypothesis" model—the one where your immune system weakens without exposure—getting a cold makes you less likely to get the flu. That doesn't appear to be true. In reality, since the cold and the flu aren't biologically related, one does not confer immunity for the other.

That's not to say the "hygiene hypothesis" is completely false. There's good evidence that exposing children to low level pathogens early and often helps reduce autoimmune conditions like allergies, asthma, and arthritis. It just doesn't effect viral response.