Trouble understanding overlapping genes.
A gene has got nothing to do with a stop codon. As you might know there are non-coding RNAs as well and the genomic regions responsible for transcription of these RNAs are also called genes. 

Genes that have an overlap in their genomic locations (without considering the strand orientation) are called overlapping genes. 

In case of same strand overlaps, the genes should have a different transcription start/stop site. Alternatively spliced RNAs are not considered overlapping transcripts. In certain cases, transcripts with an alternative transcription start/stop site are not considered separate genes but rather, isoforms, especially if the gene produces an mRNA and the alternate transcription start/stop sites just affect the untranslated regions (UTRs) and not the coding region (have a look at this article). 

Your confusion is quite valid and gene nomenclatures need some redefinition/clarification.