There is a mysterious factor when compute coeffiencts
It sounds like you're comparing the coefficients for two different filters:


A fourth-order Butterworth filter designed for cutoff frequency $f_c$
A cascade of two second-order Butterworth filters, each designed for cutoff frequency $f_c$.


The two are not equivalent to one another, although in the passband and stopband you will see similar magnitude responses. Specifically, at the cutoff frequency $f_c$, you'll see 6 dB of attenuation from filter #1, while filter #2 would give you 12 dB. Therefore, it's not unexpected that you would get slightly different coefficients for the two implementations.