Usually, customer receive only a single device when they buy an
Internet connection from an ISP. This device is connected to the ISP
via fiber or a DSL line, has several Ethernet ports and provides
You are looking at this from a home networking perspective, and that is not usual for a business. Typically, a business will provide its own networking equipment, and that is the CPE that connects to the DMARC (demarcation point), which can come in as any of various WAN technologies, depending on what the business ordered from the ISP. xDSL is less common for businesses than for residential users because it is too unpredictable for many business uses.
DCE and DTE are as far as I understand the two ends of a serial line,
and usually the DCE is a DSL modem that provides connectivity toward
an ISP and the DTE is most of the time a router.
DCE can be something like a CSU/DSU, modem, ethernet switch, etc. That is a communication device, while DTE is an end-device, such as a PC, router, etc. DTE connects to DCE. The most common example is a PC with an ethernet connection (DTE) that connects to an ethernet switch (DCE). Connecting two like devices (DCE-to-DCE or DTE-to-DTE) used to require a crossover cable, although most modern devices have built in the hardware and logic to detect this situation and adjust one end or the other so that a crossover cable is no longer necessary.