Despite both Seurat and monocle using
Rtsne there are a few reasons the plots you got are different:
Assuming you have used their respective standard pipelines on your data: they have different pipelines which will alter the data considerably, especially in the QC part.
They are using different seeds: in
Seurat::RunTSNE you can change the seed from the default value of 1, whereas in
monocle::reduceDimension the seed used is 2016. You could try changing Seurat's seed to 2016 and see if you can get something closer to that of monocle, although, due to the previous point, it may not happen.
Lastly, keep in mind that in
Seurat::RunTSNE you can change the parameter
tsne.method in order to use a different function other than the default