This entire discussion hinges on the supposition that Orcs and Half-Orcs are these fixed, immutable quantities, and that when you use either term, everyone automatically knows precisely what you mean down to the tiniest nuance.
In reality, different DMs have very different ideas of what an Orc is. To some, they are irredeemably evil and therefore unsuitable as a PC race. To others, they are merely primitive humanoids with aggressive tendencies but every bit as much potential for heroics as any other sentient being. And to yet others, they are basically just uglier humans with a certain reputation.
The fact that Half-Orcs are a distinct race indicates that the designers of 5e do not see them as identical to Orcs. You may disagree with their design, but if so, you've wandered off into homebrew territory. You might as well ask the forums why unicorns exist or why hags don't dissolve in the rain.