You can find a great article about this here.
basically, these two groups are very similar in their effects, however they work through different pathways.
Mitogens directly promote cell to get through G1 checkpoint through highering the activity of cyclin D/cdk4 (the complex needed to get through the checkpoint.) and according to the article above, also the cyclin E/cdk2 complex (which helps cell to get into S phase). By activating the MAPK (mitogen-activated protein kinase) pathway leading to production of transcription factors (Elk-1, jun, fos), which then promote specific transcription of proteins needed to get through cell cycle.
The mitogen pathway also causes phosphorylation of Rb (Retinoblastom) protein, which then dissociates from E2F transcription factor. This activates the E2F, which in turn helps synthesise proteins needed to promote S phase.
Growth factors usually stimulates mTOR receptor, which is a "serine/threonine protein kinase that regulates cell growth, cell proliferation, cell motility, cell survival, protein synthesis, autophagy, and transcription." Source
mTORC complex generally promotes translation. It plays role in "cell growth via the modulation of protein synthesis in yeast and mammals, it and its yeast homologs strongly stimulate transcription from all genes involved in ribosome biogenesis, transcription of rRNA genes by RNA polymerase I (Pol I), transcription of ribosomal protein genes by RNA polymerase II (Pol II), and transcription of tRNA and 5S genes by RNA polymerase III" and many other effects. Source.
Although all of this, in practice, I've seen many people use this categories interchangeably or referring to mitogens as a subgroup of growth factors.
I hope this helps.