With the current information given, the difference between the wired connection through a router and without a router cannot be definitely answered. I want to mention one more possibility: MTU issues. I'll try a gentle description of the problem.
The connection between a router and a modem may be established via PPPoE. PPPoE adds an additional header to every transmitted packet, lowering the maximum possible payload (data) size. If some communication participant along the way does not know about this and sends IP packets with the usual maximum size of 1500 Bytes, the packet has to be fragmented before entering the PPPoE tunnel. Fragment reassembly at the receiver can cause latency jitter, which may be interpreted as a connection being close to its capacity limit, causing slowdowns.
Now, if you connect your laptop directly to the modem, your laptop should know about the correct MTU since it is the one that established the connection, making this explanation somewhat unlikely. However, the fact that there is a lower-than-normal MTU on the tunnelled connection may have been forgotten by whatever PPP implementation you are using.
Lastly, why would this issue not appear with the router? Most routers are aware of this kind of problem and "clamp the MSS", meaning they use a hack one layer above IP: to participants establishing a TCP connection, they indicate that the maximum acceptable TCP segment size is lower than usual (by modifying the connection establishment packets), effectively bringing down the size of IP packets being used for that connection.
Because the router works on the LAN, probably Ethernet, and the modem works on the WAN. – user207421 – 2019-05-02T10:40:56.570
@user207421 except that in most SOHO routers the destinction between a WAN and LAN port is quite arbitrary - especially as they arethe same inteface.type, same chipset and indeed I have turned WAN ports into LAN ports and vv (usong dd-wrt) – davidgo – 2019-05-02T11:42:16.437
8When you plug direct to the modem does the ethernet adaptor negotiate full duplex? – J... – 2019-05-02T12:45:49.117
5Also which router/modem are you using? I would imagine a router would have dedicated hardware for things that your computer would do in software. Additionally, what type of connection and modem? Is this an ADSL modem? VDSL modem? Is this a copper or a fibre optic line? How is the laptop connected to the modem? USB 2? USB 3? USB-C? Ethernet? – Tom J Nowell – 2019-05-02T13:53:37.080
1@tomjnowell This is typically incorrect. The vast majority of SOHO routers do routing in software (ie using Linux and an embedded CPU). The router has to be an Ethernet / Ethernet.router based on the description. – davidgo – 2019-05-02T19:22:48.270
Are you connecting your laptop directly to the modem with USB instead of ethernet? (If so, is it using USB1.1 speed?) Is the router still connected and powered on when you're bypassing it? Maybe your ISP does something different with multiple MAC addresses connected to the cable modem. – Peter Cordes – 2019-05-02T21:14:52.060
5You should probably give a few more details, including: the brand and model of the modem, how you connect your laptop to that modem, how you connect either of the routers to the modem, what settings you have in your router for the WAN connection (including things like PPPoE). Many "modems" are actually routers, so the settings of the modem could be useful as well. What type of connection is it (fiber, cable, DSL...)? Are you sure your laptop is actually going through the modem and not via some mobile hotspot or a distant Wi-Fi network? – jcaron – 2019-05-02T23:23:14.457
what test exactly are you running to determine the speed? Answer to this will provide more info for troubleshooting. – Matija Nalis – 2019-05-03T11:40:32.200
1It would really help to know what kind of connection and hence modem you are using. If possible provide the modem and router brand and model as well. To exclude certain problems, (1) reboot both devices after connecting them; (2) try different cables (3) try different computers. Tell us what happened. – Peter - Reinstate Monica – 2019-05-03T12:02:13.333
What ISP? What make and model of modem? Did the ISP furnish the modem, or did you? These things matter. Please [edit] your question to tell us. – O. Jones – 2019-05-04T11:33:53.163
We cannot answer objectively with more details on your side. You do not tell us whether there is a USB interface or a bridged interface. i.e. my 4th LAN port in my ISP modem is bridged and much faster than going over NAT+firewall+routing of the slow ISP modem and got knows whatever else. The question is basically asking people to guess the network setup. Is it out of the equation asking this to the ISP? They ought to know their equipment. – Rui F Ribeiro – 2019-05-04T20:12:32.560