- I am writing this letter to invite you to my town.
- I write this letter to invite you to my town.
What is the difference between these two sentences?
In a context like this there is no substantive difference between the simple present and the progressive present: both designate a current activity.
In Present-day English, however, the simple present 'marks' the utterance as distinctly formal; it would be used, for instance, in a legal or bureaucratic notice (We write to inform you . . .), or in an academic paper (What we suggest, then, is that . . .). In more casual communications the simple present is usually reserved for habitual or repeated activities which have been and will be performed during an era which extends beyond the current timeframe (He writes for the Journal), and current, temporary activities are expressed with the progressive (He's writing for the Journal these days).
The first sentence is quite normal. The second sentence is a bit formal sounding. Perhaps too formal for this particular sentence.
We often use the present simple when our act of communication itself performs some kind of official function:
... and so forth. Even though the pronouncing, informing, dubbing, naming and calling are happening right now, we use the present simple because of the special function of the utterance or writing.
The important factor which allows us to use the present simple here is that the actual act of speaking or writing itself is literally performing the pronouncing, informing, dubbing, naming or calling. We could introduce each sentence with the words "By my act of speaking (or writing), I hereby ..." Consider:
Note that this can sound quite official and pompous.