委托

这里是一个开始

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const content = document.getElementById("content");
document.getElementById("nav").addEventListener("click", function(e) {
  const tgt = e.target;
  const id = tgt.dataset.id;
  [...content.querySelectorAll("div")].forEach(div => {
    if (div.id !== id) div.classList.add("hide");
  })  
  document.getElementById(id).classList.remove("hide");
    
})

content.addEventListener("click", function(e) {
  const tgt = e.target;
  if (tgt.classList.contains("close")) {
    tgt.closest("div").classList.add("hide")
  }
})

.hide {
  display: none;
}

<div id="nav">
  <a data-id="link" href='#'>One</a>
  <a data-id="video" href='#'>Two</a>
  <a data-id="images" href='#'>Three</a>
</div>

<div id="content">
  <div id="link" class="hide">
    <button type="button" id="save1">Save 1</button>
    <button type="button" class="close">Close 1</button>
  </div>

  <div id="video" class="hide">
    <button type="button" id="save2">Save 2</button>
    <button type="button" class="close">Close 2</button>
  </div>
  <div id="images" class="hide">
    <form>
      <input id="upload" value="Upload 3" />
      <button type="button" class="close">Close 3</button>
    </form>
  </div>
</div>

您可以将您的一些冗余代码归纳为一个函数，并将参数传递给它。

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function openAndClose(classBlock, classNone, classNone1) {
  document.getElementsByClassName(classBlock)[0].style.display = 'block';
  document.getElementsByClassName(classNone)[0].style.display = 'none';
  document.getElementsByClassName(classNone1)[0].style.display = 'none'
}

function closeForm(){
  document.getElementsByClassName('open_link')[0].style.display = 'none';
  document.getElementsByClassName('open_images')[0].style.display = 'none';
  document.getElementsByClassName('open_video')[0].style.display = 'none';
}

<a onclick="openAndClose('open_link', 'open_images', 'open_video')" href='#'>One</a>
<a onclick="openAndClose('open_video', 'open_images', 'open_link')" href='#'>Two</a>
<a onclick="openAndClose('open_images', 'open_link', 'open_video')" href='#'>Three</a>


<div class="open_link" style="display: none;">
<button onclick="closeForm()">Save 1</button>
<button onclick="closeForm()">Close 1</button>
</div>

<div class="open_video" style="display: none;">
<button onclick="closeForm()">Save 2</button>
<button onclick="closeForm()" >Close 2</button>
</div>

<form class="open_images" style="display: none;">
<input onclick="closeForm()" value="Upload 3"/>
<button onclick="closeForm()" >Close 3</button>
</form>

尝试使用您自己的id和类br>.open是div到openbr>target的id是您的div的id，您使用的是类

document.querySelectorAll(".open").forEach(div => {
        div.onclick = (e) => {
            switch (e.target.id) {
                case "open_link":
                    openLink()
                    break;
                case "open_video":
                    openVideo()
                    break;
                case "open_images":
                    openImages()
                break;
            }
        }
    })