Adapter
In short: In general, a connecting piece that makes two different interfaces, ports or protocols compatible.
In more detail: In a networking context, often a network adapter (the network card itself, wired or Wi-Fi); in a hardware context, for example, a USB-C-to-HDMI adapter. The common denominator: an adapter changes nothing about the content of the transmitted signal, it only adapts the physical or logical interface.
In Depth
Passive vs. active
Adapters can be roughly divided into two groups: pure plug adapters that only change the physical form but pass the electrical signal through unchanged (e.g. a USB-C-to-USB-A adapter that merely adapts the pin assignment), and active adapters that actually convert between different signal formats or protocols (e.g. an HDMI-to-VGA adapter that converts digital into analogue signals and needs its own chip with its own power supply for this). The difference matters in practice: a pure plug adapter almost always works losslessly and is usually much cheaper; an active adapter can bring additional latency, quality loss or power consumption — and basically only works in one direction unless explicitly advertised as bidirectional (an HDMI-to-VGA adapter, for example, usually does NOT also convert from VGA back to HDMI, because the digitisation of an analogue signal required for this is technically more complex than the reverse).
A related but different category is dongles and active cables with built-in signal conversion, such as DisplayPort-to-HDMI adapters, which rely on so-called “DP++” outputs to work passively — if the source device lacks this capability, an active (powered) adapter is absolutely necessary, otherwise the screen stays black. The same applies to USB-C docking stations, which internally multiplex several protocols (USB, DisplayPort Alt Mode, sometimes Thunderbolt) over the same physical socket.
Network adapter (NIC)
In a networking context, the “network adapter” (also network interface card, NIC) is the hardware component that makes a computer network-capable in the first place — today usually integrated directly into the mainboard, formerly a separate PCIe expansion card. It handles the conversion between the computer’s internal data buses and the physical transmission medium, whether Ethernet cable or Wi-Fi radio, and is thus the interface between layer 1 (physical) and layer 2 (data link) of the OSI model: it converts electrical signals or radio waves into frames and carries a globally unique MAC address burned in at the factory.
Modern NICs increasingly take over tasks that the CPU used to have to handle — so-called hardware offloading functions such as TCP checksum calculation, segmentation of large data packets (TCP segmentation offload) or even parts of the encryption directly on the network card’s chip. On servers with very high data throughput (10/25/100 GbE), this makes a noticeable difference to CPU utilisation.
Common sources of errors in practice
Auto-negotiation problems (where two devices can’t agree on the same speed/duplex setting) are a classic cause of seemingly “inexplicably slow” wired connections despite a correctly connected adapter — usually recognisable by error counters (CRC errors, collisions) in the network driver statistics. With USB network adapters (e.g. USB Ethernet dongles on laptops without their own Ethernet port), the bandwidth of the USB port itself is also a limiting factor that is easily overlooked.