BLS?

BLS is a regional Swiss Train Operator. Like MGB, Raethian Railways and a few others.

For all purposes, they all operate under the same general ticketing and timetabling system (which you can get from SBB), but they do sell some specific passes (such as the Bernese Oberland Pass) or SBB tickets that might get around restrictions on credit card processing.

BLS is an acronym for the rail company - owned by the Canton of Bern and the country of Switzerland comprised originally of the Bern - Lötschberg - Simplon Railway and now comprising much more territory.

They run the local S-Bahn services in and around the city of Bern, and the line through both the Simplon and Lötschberg tunnels, as well as the new Basis-Tunnel; they run through the Emmental to Luzern, and into the French language region west of Bern. They have the line from Bern to Interlaken, and they operate the steamers on both Lake Thun and Lake Brienz.

BLS AG owns or operates on the following railway lines:

Bern–Neuchâtel railway line
Grenchenberg railway line
Gürbetal railway line
Hauenstein railway line
Lake Thun railway line
Lötschberg railway line
Spiez–Erlenbach–Zweisimmen railway line

They also issue the Berner Oberland Pass.

In all other aspects they are pretty much interchangeable in the area with the SBB. All of their services appear on the SBB web pages and app, like all operators in Switzerland.

Thank you both very much!

BLS = Bern–Lötschberg–Simplon
It is one of Switzerland's many railway companies, actually the second largest after the SBB.
As the name suggests, they run one of the two main lines through the Alps to Italy (via the Lötschberg and Simplon tunnels), plus most of the local trains in the Bern Area including to Interlaken.
See Wikipedia here: https://en.wikipedia.org/wiki/BLS_AG

As far as a tourist is concerned, they do not need to know railway company is which, apart from the trains being a different colour.
The rail companies are all integrated, the trains all connect regardless of which company is involved and they run on each others lines where necessary.
Tickets are the same for all companies, they share the money between themselves.
The SBB website gives info for, and sells tickets for, all companies. You have no need to use the BLS site (EXCEPT for booking the car-transporter service through the Lötschberg tunnel).

If you want to, for example, go from Interlaken to Bern, you just buy a ticket, and it will be valid on all trains, either the InterCities heading to Zürich, with "SBB" on the side, or on the BLS local trains to Bern.

Photo of a BLS train: https://www.bls.ch/-/media/bls/bilder/unternehmen/projekte-und-hintergruende/dossiers/rollmaterialbeschaffung-flirt-re-kandersteg-winter.jpg

Many thanks for the details, Chris!