When you want two programs to pass data to each other on their own, with nobody copying by hand, there are two roads. The difference between them is simpler than it looks.
The direct integration
Some programs are built to talk to the outside. They have a service door, usually called an API, or they accept a file to import, or they read and write to a database you can get into.
In those cases no screen has to be opened at all. The data goes in and out in the format the program expects, and the program treats it as if an operator had typed it in.
The advantage is stability. A service door rarely changes, and when it does the software maker usually writes it down somewhere, so you find out before anything breaks. It is also fast, because nothing has to wait for a window to open.
The limit is that this door has to really exist, and it has to do what you need. It is not rare to find an integration that reads the data but does not write it, or that covers the customer records and not the documents. Then half the work is left uncovered.
Working through the screens
If the door is not there, the system does what a person would do. It opens the program, clicks the right menu item, types into the fields, presses save and reads the confirmation message.
This is the way that lets you automate even old business software, the kind installed on the computer twenty years ago, the kind nobody maintains any more but that half the company runs on. Nobody's permission is needed, because if a person can go through those steps, so can the system.
The limit is that it depends on how the screens are built. If an update moves a button or renames a field, the steps have to be adjusted. That is why work done this way needs checks, a log of what it did, and a stop that halts everything when something does not add up, instead of carrying on and filling your business software with wrong data.
What really changes between the two
The difference is not the quality of the result. The data that ends up in your business software is the same. What changes is what you depend on, the software maker or the windows in front of you.
The screens give you much more freedom, because anything you can click can be automated, and you pay for that freedom with a little more maintenance.
How to choose for your process
If the direct integration exists and covers the piece of work that weighs on you, that is where we start. If it does not exist, or covers only part of it, the screens do the rest.
Before deciding it is worth looking at two things about the program, whether it has a documented way to import or export, and how often it gets updated. Business software that changes its face every couple of months makes the screens harder to keep up with. And if you have the contact of whoever sold you the software, one straight question to him saves a lot of trial and error.
It almost always ends up a mix
In practice a process rarely sits entirely on one side. Take a made-up case, just to be clear. An invoice arrives as a PDF, the system reads the document and checks that the VAT number and the amounts match the order, then it writes the supplier record through an import the business software accepts, and finally it records the document by opening the screen, because for that one there is no import function.
Three different methods inside the same run, and for you nothing changes. You only see the invoice recorded.
Where to look to work it out
If you are weighing up a process of your own, very little information is needed. Which program is involved, which steps the person using it goes through today, and how many times a month it happens.
Those answers already tell you whether it is worth hunting for a direct integration or whether you may as well start from the screens. The number of operations per month is what weighs most, because on a handful of cases a year neither road pays for itself.