If you want practical examples of what they do, go to digikey.com, search for the company names and click randomly on one of the thousands of hits.
Here's a microcontroller: https://www.digikey.com/product-detail/en/maxim-integrated/M...
Here's an I2C temperature sensor: https://www.digikey.com/product-detail/en/maxim-integrated/M...
Here's an RF amplifier: https://www.digikey.com/product-detail/en/maxim-integrated/M...
Here's a 3v3 DC-DC: https://www.digikey.com/product-detail/en/linear-technology-...
As an aside, AD has a large number of parts which are non-public. You will not find the part numbers (or any information about them) without an NDA and personal assistance from an AD rep.
As a hobbyist, this sucks so much. With PCB manufacturing reliable enough for high speed signalling being affordable and hackerspaces with soldering ovens in every major cities (and there was some startup - in NYC I believe - that you could give Eagle files and a product order list and they would buy you the components at Digikey and manufacture the board for you... anyone remember their name?!), it really really sucks that all the interesting stuff is hidden beyond such obscure walls.
You won't even find Intel Thunderbolt datasheets on obscure Chinese sites. Wtf? And then Intel complains about why people aren't adopting it?
I don't know about that specific startup, but there are tons of firms in China which will manufacture and assemble PCBs for you. Most of the big hobbyist firms, like JLCPCB, Elecrow, and PCBWay, offer some form of PCBA service. JLCPCB in particular is closely integrated with LCSC, and will source parts directly from them.
Are you thinking of MacroFab (https://macrofab.com/) located in Houston? I believe they have been featured here before.
I agree that the categorization can be a bit tricky at times, but once you're used to it it's not terrible.
Also often times you'll find some great component on e.g. Maxim's website, only to find no one distributes it, so it's effectively useless in the immediate sense.
Not a microcontroller.
There is overlap, but the portfolios are complementary. It seems to be a good acquisition save the sticker price seems too high.
Maxim tends to make a bunch of almost generic odds and ends, are middle-to-low prices, with fairly large volumes. They compete directly against Texas Instruments for a lot of interface products.
This acquisition is especially interesting in light of AD's (relatively) recent acquisition of Linear Tech, which was basically a consolidation of the high-performance low-volume integrated circuit market.
Does your hardware need power? It needs power controller and converter chips, such as a MOSFET driver, a DC-DC converter, a charge pump, a linear regulator, a voltage monitor, or a power multiplexer (if it has multiple power sources). Does it have a battery? It needs a battery charging controller, or a battery gauge. Does it need to communicate via a data interface or a cable? It needs interfacing chips, such as I2C chip, SPI chip, IIO chip, RS-232/RS-485/RS-422 chips, CANbus chipss, LVDS chips, voltage level translation chips, and I/O extending chips. Does it have USB? It may need a USB multiplexer chips to switch between different signal sources (for example, USB Type-C can be an audio port or a data port), or a USB charging controller chip. Does it need wireless communication? It needs RF front-end chips, RF amplifier chips, RF frequency synthesizers, and SoCs for Bluetooth, Wi-Fi, GPS, etc. Does it need data acquisition capabilities? It needs ADC chips, DAC chips, amplifier chips, and signal conditioning chips. Does it need NFC/RFID? It needs NFC and RFID chips. Does it have a screen or a LED light, like a screen backlight or a flashlight? It needs LED controller chips and power chips. Does it need any kind of software control? It needs a microcontroller. The list goes on.
And Maxim's products cover almost all of these applications.
So does Analog Devices' products, but with an emphasize on high-precision, high-performance components.