Mismo vs. igual
In the Spanish language, mismo and igual play unique roles even though they both translate to same in English. The difference lies in how they're used in sentences and their relationship to the words or concepts they modify.
Mismo
A2Mismo roughly translates to self or same in English. The word is usually used to refer to the same person or thing mentioned earlier.
Estoy viendo el mismo programa de televisión que ayer.
(I'm watching the same TV program that I did yesterday.)
Vivo en la misma casa desde que nací.
(I have lived in the same house since I was born.)
Juan se culpa a sí mismo por lo sucedido.
(Juan blames himself for what happened.)
Igual
A1Igual can mean equal, identical, or the same as. It's used when two or more things are alike, equivalent, or have equal status or nature.
El vestido es de color azul, igual que tus ojos.
(The dress is blue just like your eyes.)
Todos los estudiantes tienen derechos iguales en la escuela.
(All students have equal rights at school.)
Tiene una actitud igual a la de su madre.
(He has an attitude identical to his mother.)
Summary
While both mismo and igual can be translated as same, they have different uses in context. Mismo refers more directly to something previously mentioned, indicating that it's exactly the same thing or person. On the other hand, igual is used to highlight likeness, equality, or similarity among things, people, situations etc.