Deomai is a strong way to ask for something - a leper imploring Jesus to heal him (Lk ), a father's desperate plea to Jesus to cast a demon out of his son (Lk ).
The idea can be to desire something, with the implication of a pious wish.
Deesis prayers arise from one's sense of need (which reflects a humble heart) and in knowing what is lacking.
This individual's plea is in turn made to God to supply for the need.
In Classical Greek deesis (in contrast to the Biblical uses) was not restricted to sacred uses, but was employed of requests preferred to men.
)(proseuche from pros = toward or immediately before euchomai = to pray or vow) is the more general word for prayer and is used only of prayer to God.