As far as I know, they're identical. And are both grammatically correct and can be used interchangeably.
Is this indeed the case?
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They can be identical in meaning, but that's not always the case.
No puede conectarse may always be rendered as No se puede conectar due to the phenomenon of pronoun raising of Spanish. In this case, the se is associated with the verb conectar, but may be placed either with conectar (enclitically, because it's in the infinitive) or poder (proclitically, because it's conjugated).
However, se need not necessarily be associated with conectar. It is also possible that the se is associated with the verb poder, forming an impersonal statement. In this case, because pronouns can only be raised and not lowered, there is no other alternative rendering and only "no se puede conectar" works.