Multivariate models - standard error help

I have 2 multivariate models created in R concerning nutrition

Model 1 = -11.5±1.68 + 0.56±0.562 Intake + 16.6±0.165 Potassium concentration

Model 2 = 16.6±0.123 Potassium concentration

Both of these have come from the same data set. My question is, is it right that the standard error is different for potassium concentration in the second model than in the first? If they came from the same dataset, then I would assume the SE's for both would be the same, but I am not too familiar with R, therefore am wondering whether the addition of 'Intake' to the first model could have interacted with potassium conc and therefore changed it's SE?

Thanks for any help!