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The real scripture: 59 And they stoned Stephen, calling upon God, and saying, Lord Jesus, receive my spirit. This is not a transcription, the writer wrote this down years after the event had occurred. I only know that Stephen was being stoned to death, I doubt if he could utter a formal prayer while people where beating him in the head with large rocks...He was calling to Jesus whom he could see. I explain more below.

Are you claiming that if somebody whispers upon the name of Jesus, that might be prayer; but if someone openly & publicly & directly calls unto Jesus, well that's somehow clearly not prayer?

(Your parsing is at least humorous...I love getting such prompted smiles)

Perhaps the most literal translation of the word (in context) is: "a calling upon unto"
Westcott & Hort GNT - Literal Translation: Acts 7

The Greek word in question is: epikaleo per lexiconcordance.com

The various contextual usages of this word is simply "call" as it's etymologically tied to the Greek word "kaleo" and it includes to "invoke" (as how the Name of Jesus was invoked/called upon in Acts 9:14) or to "appeal" ... as in Acts 25:21 and 28:19 where it is used to appeal to the highest governmental authority (Caesar).

Prayer or "pray" is simply an overall umbrella word used in the Scriptures for ALL types of communication with God. In the Scriptures, we find various types of prayer...for example (not meant to be exhaustive):
* Confession
* Thanksgiving
* Supplication
* Intercessory (on behalf of others)
* Blessing
* Imprecatory (numerous psalms)

Believe me, if I am a judge in a courtroom, I would eventually receive ALL of these (& other) types of communication from the parties involved...
...confessions of crimes,
...thanksgiving from victims that justice was served,
...intercessory pleas to be lenient on those to be sentenced,
...and just the opposite...others who rein down imprecatory condemnations upon the guilty, asking that I toss the book at 'em...

And guess what? Appeals would be part of that process, too.

And yes, if I was Lord Jesus, somebody calling me, appealing to me, etc. IS talking to me and IS expecting a response based upon authoritative Lordship!

But, hey. A "C+" for "effort" on a legalistic attempt to narrowly define communication with the Lord Jesus!