Dear student
Anode rays differ from cathode rays in several aspects and their specific charge(charge/mass or e/m ratio) is an important feature. The reason lies in how anode rays are produced. Anode rays are produced when a gas at low pressure is subjected to a high voltage(10,000 Volts). Under these conditions, the atoms of the gas get ionized, i.e. they lose some electrons and thus become cations(positive ions).

It is a stream of these positive ions that become 'anode rays'. However, the atomic masses of different gases are different and hence, the mass of anode ray particles varies when you use different gases in the discharge tube and hence, the charge/mass ratio also varies.

Whereas, in the case of cathode rays, the cathode ray particles are nothing but electrons. Their charge and mass is constant no matter what gas you use in the discharge tube. So, their charge/mass ratio remains constant.