I have a problem in understanding what is the standard approach to follow for editing office documents inside my document library. As it seems each browser will have different behavior when it comes to editing office documents. For example, using IE browser, there are two ways to edit office documents as shown in the below two picture, mainly either; clicking on the "Edit" link from the drop-down menu OR view the office document inside the browser and click on "open in excel" or "open in visio" links.
After that I can edit the office documents using my client applications (Excel or Visio) , and when I choose to save the documents, the updated version will be automatically uploaded to the SharePoint document library. However, when using Firefox I will not be able to automatically save the documents from my client excel application or my client visio application to SharePoint document library. So can anyone advice why I have this differences? Thanks