As noted above, it is common for bacteria to share identical genes across various strains or even species, sometimes by horizontal transfer and sometimes by conservation. But if two bacteria have identical complete genomes (including plasmids) they are surely the same strain/isolate. Bacterial nomenclature can be strange in some cases, so for example if a human is killed from botulinum toxin the bacterial isolate will most likely be designated as "Clostridium botulinum" but if a highly related isolate was obtained from soil and not known to produce toxin, it might be designated as "Clostridium butryicum". And it is rather common for very important clinical or biochemical features such as toxin production to be carried by plasmids which can be gained or lost or transferred between species.

Bernice Mae Yu Jeco-Espaldon

Like Brian Thomas Foley said, there are very common for two strains of bacteria or different animals/plants to share identical genes or genes with very conserved sequences. On the genome level, it is also possible two 'strains' (or subtypes) share very similar genomes. These can be due to mutations, such as the COVID-19 caused virus, SARS-CoV-2. They already have several 'strains' (subtypes) existing now after only a few months' of mutations.

Indeed yes. And not just strains. Some species of Pseudomonas share identical 16s rRNA sequences.

There are two possibilities in this situation:

1. Since there are two strains, so there must be some difference that's why they are categorized as different strains.

2. The two strains could be genetically similar but due to variation in the outside conditions, they might have been expressing different genes and hence due to the visible or countable differences, the strains could have been categorized.