I've been reading lately about primary (which I understand completely) and secondary (which I do not understand that well since I'm not very good at chemistry) structure of proteins. My question is: Can two proteins have equal primary structure but different secondary structure?
By equal I assume you mean identical.
Yes, in fact several known proteins have different folding patterns for the same primary structure as part of their function. but most proteins can take on more than one folding pattern, in fact specialized proteins called chaperones exist to encourage (force) a particular folding pattern in some other proteins, especially ones that are essential or in which the other foldings can be dangerous.
The easy way to understand the difference is the primary structure is the amino acid sequence and the secondary is the first stage in how the protein folds (the other being the tertiary). the primary creates the secondary (and tertiary) but there is usually more than one stable folding.
this video contains a further breakdown of the different levels of structure.