I know of 2 ways for taking and editing screenshots on Chromebook that is similar to the Snipping Tool app on Windows.

First way, click on the clock in the lower right corner and click on the Screen Capture button. There you will have options to take the full screenshot, a part of it / rectangle, or the active window only. After using one of these, the screenshot will be captured and there will be a pop-up window in the lower right corner with the screenshot image and an Edit button. Click Edit for more editing functions like on the Snipping Tool.

2nd way - keyboard shortcut CTRL + Show Windows key (a key marked with a rectangle with 2 lines besides it). Then again Edit button if you need further editing.