✓ Accepted answer
The "player model" you're referring to is more fittingly called the Character. The Touched event's only parameter is the part that touched. This means that, if a player's character touches it, the character model will be part.Parent. These are examples with :GetFullName(), which returns a string displaying the object's ancestory.
local part = workspace.Part
part.Touched:Connect(function(otherPart)
print(otherPart:GetFullName())
end)
The MouseClick event of ClickDetectors has one parameter: the player who clicked (the object in the Players service, as you said).
local part = workspace.Part
local ClickDetector = part.ClickDetector
ClickDetector.MouseClick:Connect(function(player)
print(player:GetFullName())
end)
Don't be discouraged when you're not sure of the parameters of an event. Short of guessing, you simply cannot know until you search them on the wiki!
##Resources:
MouseClick
##Accept and upvote if this helps!