Nope. Islam does not make this distinction.
Per Islam, prayer is an act of worship. 'Humans' are acknowledged as created beings who themselves are helpless so to think they have any kind of power or influence to 'grant' people their requests is not right. The only one to whom prayers and worship should be directed to is God.
ولا تدع من دون الله ما لا ينفعك ولا يضرك فإن فعلت فإنك إذا من الظالمين
Translation: (And do not invoke besides Allah that which neither
benefits you nor harms you, for if you did, then indeed you would be
of the wrongdoers) - Qur'an 10:106.
Furthermore, when saying 'peace upon you, O Prophet' we do not believe that he directly hears this from us. Rather, the Angels hear it and convey this message to him. And as for saying 'peace be upon you/him'.... all peace comes from Allah (ﷻ).
Thawban narrated that when he finished his prayer, the Messenger of Allah (ﷺ) would ask for forgiveness three times, then he would say:
“Allahumma Antas-Salam wa minkas-salam tabarakta ya Dhal-jalali wal- ikram” (O Allah, You are As-Salam and from You is all peace, Blessed are You O Possessor of majesty and honour)” - Ibn Majah (928).
Basically, there is no element of beseeching anyone other than Allah (ﷻ).