A null-picovoltmeter converted into a highly sensitive magnetometer is used for the first time to compare the temperature behavior of magnetic and resistive transitions into the superconducting state of samples of the iron-containing compounds FeSe (single crystal) and LaOFFeAs (granular) with the same transitions in a classical single-component superconductor (Pb). It is discovered that the temperature behavior of these transitions in the iron-containing superconductors differs thermodynamically from their behavior in Pb, and radically so in the case of the granular LaOFFeAs samples. It is also found that the magnetic susceptibility of FeSe in the non-superconducting state has a positive sign indicative of ferromagnetic ordering of the local spins of the iron ions, while the susceptibility of the LaOFFeAs samples in this state remains diamagnetic. The observed features of the superconducting transitions are analyzed.