Firstly, these don't look like the same font, and they are not the same weight. Sometimes companies will have a custom font designed specifically for them, which may not be available to the general public for download. Sometimes a designer can also modify existing letter forms for a one-off custom design.
To edit the letter forms you would need to turn the text to outlines.
In Illustrator you can do that using Object > Expand or Type > Create Outlines.
You can move anchors by selecting them with the Direct Selection Tool (A).
In Illustrator CC* you can round corners by selecting and moving the rounded corner widget.
In Inkscape you can turn text to outlines using Path > Object to Path
You can move the nodes by selecting them with the Edit Paths by Nodes tool (F2). You can add nodes by double clicking on the path, and change nodes to smooth nodes in the Tool Controls Bar along the top, and adjust the Bézier handles
*Note: If you don't have Illustrator CC with the round corner widget functionality, you can use the same technique described for Inkscape. Add anchors using the Add Anchor Point tool, convert to smooth in the tool options along the top, and adjust the Bézier handles.