We generally use 'equal' for numbers. For example, if there are 15 boys and 15 girls in a class, you would say that there's an 'equal number' of boys and girls. But if you like watching romantic comedies and your friend likes them too, you would say that you like the 'same kind' of films. You couldn't use 'equal' here.

If two things are equal then they are exactly the same proportion. "The movie was equally sad and funny." Meaning that it was both sad and funny to the same degree. "My sister and I have the same haircut." Our hair looks similar. The word "equal" is more exact than the word "same".