If I'm not wrong, there are multiple service providers that cover different areas in Brussels. Is there any pass that covers all of them? Or do I have to buy a separate one for each different service provider?
There are four operators of public transportation active in Brussels. However, most people only need one. But if you would have to change between operators, a ticket covering them all is available.
- STIB/MIVB: this is the specific operator for Brussels. They operate all trams in Brussels, the metro and a dense bus network. In general you will only need this one inside Brussels.
- SNCB/NMBS: this is the operator for all Belgian trains. So this includes the trains inside Brussels. In some case they will be a lot faster than the STIB/MIVB network. I'm specifically thinking about traveling between Brussels-North and Brussels-South railway stations.
- De Lijn: this is the Flemish bus operator. Brussels is not Flanders, but some of their lines end in Brussels, most of them at the Brussels-North railway station. I don't see a case where you really would need them, but you never know.
- TEC: this is the Walloon bus operator. The story is similar as for De Lijn: some of their lines have a terminal in Brussels. From where Wallonia is located this is obviously mainly in the Southern part of Brussels. Similar as for De Lijn, they are very unlikely to be useful for you.
As complicated as this all sounds, it is a lot more easy if you are interested in the tickets. Just take a look at the fares of STIB/MIVB. Every ticket with "JUMP" in the name is valid on the entire network of STIB/MIVB (with the exception of the airport) and on the networks of SNCB/MNBS, De Lijn and TEC inside Brussels. The single tickets, return tickets and passes for a few days all have "JUMP" in their name. So you're good with any of those.
Only if you want to travel outside the borders of Brussels with either SNCB/NMBS, De Lijn or TEC will you need to buy another ticket with the relevant operator.
For completeness, I'll add a few words on the airport. The airport is not located in Brussels, but in Flanders. I've mentionned before that the airport is not covered by a normal STIB/MIVB ticket. As is often the case with airports there is a special (more expensive) fare for that. On the page with fares for STIB/MIVB that I linked to above, just look for anything with "Airport" in the name. There are trains from the airport to the city, but they also come with a surcharge and are SNCB/NMBS specific. There are also buses of De Lijn to Brussels. On those you only pay the standard fare, but they take ages and you will need to buy a ticket from De Lijn. In short, if you only visit Brussels, the airport is normally the only place where you will be confronted with a choice between the tickets of different operators.
And if you are flying to Charleroi (Brussels South Charleroi or however they may call it nowadays) we are opening another can of worms because it is so far from Brussels.
Public transport in Brussels is run by one organisation as far as I can tell. Certainly I have used buses, trams and the metro using the same card
If you are there for a visit you might want to get the Mobib Basic card as outlined in the link I show. You have to pay a deposit and then load it with various options: single journeys, five or ten journeys, day tickets, ... If you have the five or ten jourey option loaded you can share the card between passengers.
If you want to travel outside Brussels the position is more complicated as you need to investigate De Lijn https://www.delijn.be/en/ which covers services in Flanders.
Coincidentally, I was in Brussels just a few days ago and can confirm that only a single ticket is needed. You can buy them from automated kiosks in any metro station and they give you plenty of options with various number of trips and validity periods.
For a day or even two, depending on the purchase time, buying the 24h card is very cost effective. Your 24h will start on the first tapping at the entrance of metro, tram or bus and each time you tap, it will tell you how much time you have left on the card. The cost is about 7.5 Euros IIRC.
Getting out of the city or commuting between train stations, as I've seen many people do, takes another type of ticket but the metro reaches the train stations too or close by, so this is not really needed within Brussels.