Yes, especially with WiFi. Old routers can also give slow WiFi. 802.11g has an instantaneous speed of upto 54 Mbps, which means that you are unlikely to get an average much over 20 Mbps. 802.11b has an instantaneous speed of upto 11 Mbps which might give you an average of up to around 5 Mbps.
The same is true for older Ethernet connections. The very early ones achieved 10 Mbps while later ones offer 100 Mbps. This is still the most common speed, although there are many recent devices that can achieve 1000 Mbps (1 Gbps). Ethernet should be able to maintain average speeds of around 85% of the specified speeds.
Internet connection speeds are limited by the slowest link in the chain. A 75 Mbps ISP connection going through an old router offering 802.11g WiFi to a laptop with a 802.11n adapter (capable of 150 Mbps), is unlikely to get much over 20 to 25 Mbps on a speed test - the average speed for the slowest component - the 54 Mbps instantaneous speed of the 802.11g router. Similar things can happen with Ethernet.
With WiFi, if a slow device is connected to a WiFi network, it can drag down the speed of the whole WiFi network, not just the one slow device.
I hope this helps.