I've heard sometimes that イコール is used sometimes to imply that things are similar. What would be a correct expression to use イコール? Furthermore, how is it different from using 同じ to say that things are similar?
イコール is "equals", and 同じ【おなじ】 is "same".
The terms have exactly the same implications as they do in English. You could even say they are equal to their English counterparts. ;)
AとBは同じです means that A and B are similar. They are two different things.
AイコールB means that A and B are a unique thing, with two names.