In short, the difference is that PIs can't do all the things an EMI can do. Both need to maintain certain adequate capital and segregate customers' balances, so in terms of safety of funds, there shouldn't be any difference. But a PI can't hold a balance for a customer for any significant length of time, so the funds need to either be held with a partner bank (akin to a correspondent account) or be quickly moved to another financial institution. There are other differences between PIs and EMIs, too.
For an example, you can see the difference by visiting the two links I posted and compare the different activities with Paysera, which is a well-established and mature EMI.
I am not advising anything.