Don't they both just disrupt RNA so it can't make a protein? If so, then what is the difference between the 2?
Antisense simply means that a sequence is the complement of another. miRNAs are naturally occurring antisense RNAs yes. The "difference" is that antisense RNA is often used for sequences developed in the lab and used for processes such as RNAi.
miRNAs, on the other hand, are encoded by the genome and are used by the cell for regulating gene expression. They do this through the RISC complex, just like artificial antisense RNAs such as siRNAs.
Basically, antisense is the general term, and can be applied to any sequence whose complement exists in the genome. miRNAs are a particular class of antisense RNAs.
Antisense RNA is any RNA that is complementary to another RNA. Therefore, miRNA is a type of antisense RNA. Antisense RNA can inhibit translation of mRNA by hybridizing and preventing ribosomal binding/translocation. Antisense RNA in this context could be any length and bind anywhere between the RBS and end of the CDS. miRNA also prevents translation but it does so through the RNAi pathway by facilitating binding of the RISC complex to mRNA (often in the 3'-UTR, which is after the CDS). miRNA are around 22 nts long (but it is species dependent).