Clearly a set of encoding rules must be such that any particular bit pattern corresponds to just one ASN.1 data structure - otherwise software receiving a message would not know which data structure to interpret the bit pattern as. However, the reverse is not necessarily the case - no ambiguity is caused if several different bit patterns can represent the same ASN.1 data structure.
Nevertheless, in some applications, if different bit patterns can represent the same ASN.1 data structure, it does cause problems. For these applications, it's desirable to have a set of encoding rules where each ASN.1 data structure converts to just one bit pattern, and vice versa. This is especially true in secure communications, because if you are digitally signing messages you need semantically equivalent messages to always have the same encoding.
Such a set of encoding rules is called canonical, or distinguished. Two such sets of rules have been developed - one was named the Distinguished Encoding Rules (DER) and the other was named the Canonical Encoding Rules (CER). CER has not caught on, and is very seldom used. However, the standard file extension for a file containing DER is .cer.
In reading documentation of OpenSSL, you will often see mentions of data stored in DER format.