The website will check your grammar and punctuation also.
- The use of "will" indicates the future, you are not finished writing yet, but when you are (in the future) it will check.
the website checks your grammar and punctuation also.
- This is describing the abilities of the website. Every time, it will always check.
the website is checking your grammar and punctuation also.
- you are finished writing, the website is currently checking now. The action is happening now.