E-file: which is essentially just an api end point for accepting digitized tax returns and is what all the major (paid) tax software uses.
Direct file: a web based version of the 1040 irs forms which will, when filled out, submit the forms electronically.
=== Edit: there are actually three, the third is Free Fillable Forms, which is what I'm actually talking about here ===
Note that when I say "version of the forms" I mean that quite literally. The interface is as close as html can come to looking like a printed 1040 form and about 1 tiny step up from filling out a pdf version.
The forms will occasionally do math for you: some of the fields are marked as the sum of a set of fields and those will automatically do the addition for you, but that's the limit of the automation.
For example, to compute your actual owed taxes you need a percentage to multiply by your taxable income, and that number is found by looking through a roughly 10 page table that maps income ranges in brackets of $50 to a specific number (so 0-50 is one number, 50-100 is another, and so on up to several hundred thousand).
To get this number for the form you, of course, must open the help documentation in a separate tab and scan through it looking for your bracket.
My understanding as to why it works this way is that the irs is basically doing as much as they're legally allowed to. The irs is, as far as i know, forbidden by law, from developing any kind of software that helps you file taxes (or more accurately, competes with turbotax) and this web-form doesn't quite count as breaking that law.
I'll note in passing, that as a general rule "both sides" tend to take turbotax money to hobble the irs, this specific direct file was championed and funded by democrats, opposed by republicans and the republican president trump is trying to delete it.