  In recent years, the focus of bioinformatics research has moved from
individual sequences to collections of sequences. Given the fundamental role of
the Burrows-Wheeler Transform (BWT) in string processing, a number of dedicated
tools have been developed for computing the BWT of string collections. While
the focus has been on improving efficiency, both in space and time, the exact
definition of the BWT employed has not been at the center of attention. As we
show in this paper, the different tools in use often compute non-equivalent BWT
variants: the resulting transforms can differ from each other significantly,
including the number $r$ of runs, a central parameter of the BWT. Moreover,
with many tools, the transform depends on the input order of the collection. In
other words, on the same dataset, the same tool may output different transforms
if the dataset is given in a different order. We studied $18$ dedicated tools
for computing the BWT of string collections and have been able to identify $6$
different BWT variants computed by these tools. We review the differences
between these BWT variants, both from a theoretical and from a practical point
of view, comparing them on $8$ real-life biological datasets with different
characteristics. We find that the differences can be extensive, depending on
the datasets, and are largest on collections of many similar short sequences.
The parameter $r$, the number of runs of the BWT, also shows notable variation
between the different BWT variants; on our datasets, it varied by a
multiplicative factor of up to $4.2$. Source code and scripts to replicate the
results and download the data used in the article are available at
\url{https://github.com/davidecenzato/BWT-variants-for-string-collections}
