Think of Digital-to-Analog Converter (DAC) as the genus and DAC types as the species.
Delta-sigma. The most common DAC type, chip-based delta-sigma DACs, employ digital-to-analog converter chips manufactured by a third party. Delta-sigma refers to the D/A conversion process wherein the binary data is first converted from its original Pulse Code Modulation (PDM) format into Pulse Dense Modulation (PDM). The signal is then oversampled, i.e. converted into a higher frequency, during the conversion process. Your phone, TV, and computer have delta-sigma DACs inside. Popular DAC chip manufacturers for hifi include ESS, AKM Semiconductor, Analog Devices, Texas Instruments, and Wolfson Microelectronics.
FPGA-based. A Field-Programmable Gate Array (FPGA) is an integrated circuit, a digital brain, that is programmed by the DAC manufacturer to perform digital to analog conversion (and other tasks). Unlike delta-sigma DACs, FPGA-based DACs do not convert PCM to PDM, rather the original signal remains PDM throughout. FPGA-based DAC manufacturers include Chord Electronics, dCS, Exogal, Playback Designs, and PS Audio.
R2R. A resistor-ladder DAC (R2R) employs a series of resistors of two values—R and 2R—for D/A conversion. The R2R network can be chip-based (multibit) or discrete (look ma no chips). Unlike delta-sigma DACs, R2R DACs do not convert PCM to PDM, rather the original signal remains PDM throughout. R2R/Multibit DAC manufacturers include Aqua Acoustic Quality, Denafrips, Holo Audio, Metrum Acoustic, MSB, Schiit, and totaldac.
Not to muddy these clear waters but some DAC manufacturers mix types, just like in The Island of Dr. Moreau (minus the negative consequences). Mix-type DACs include those that employ a DAC chip for D/A conversion and an FPGA for custom digital filters (like the Ayre Acoustics QB-9), R2R DAC for D/A conversion and an FPGA for filtering (totaldac), FPGA for digital processing before the discrete ladder DAC (Aqua Acoustic Quality), FPGA before the multibit DAC (Metrum Acoustics), and a digital signal processor (DSP) in conjunction with a multibit DAC (Schiit).