No. Menulis simply means to write, like tulis does. They can be used interchangeably.
Tulis is the root word, and menulis is the word derivated from it. (men+tulis).
Saya tulis surat = Saya menulis surat.
Maybe "tulis" more informal, and less common than "menulis", but that's all.
And Duolingo accepts both interchangeably.
Test "Kita tulis" for instance here.
For the "ing" form, if you mean "a writing" it's penulisan.
And if you mean the "ing" verbal form, it's "Saya sedang menulis/tulis".