Wired network (excluding powerline) gives you guaranteed speed, yet mesh wifi gives your wireless devices convenience & freedom using same SSID around the house without interruption when you are walking around.
A well designed standard, non-mesh WiFi network would provide the same freedom/capability to not be interrupted when you walk around. But that said, a lot of that non-interruption is based on how the client acts, not the router/access points. The reason you may experience a pause/interruption is due to bad hardware/driver implementation on your WiFi card in the computer/phone/laptop/tablet (again, assuming you have properly configured your wifi network itself).
For a properly configured non-mesh WiFi network, you need to space the multiple access points around the house/area fairly evenly. All of them are set with the same SSID, but each uses a different channel. Please note, that channel usage does overlap, so what you really want is to use non-overlapping channel selections across the various access points (which for the 2.4Ghz means using channels 1, 6, and 11, and you probably want to limit it to using only 20Mhz channel width, even though the later standards support up to 40 or even 80, almost no client cards/devices will support those and if there is even just a single device in your network's range that does not support the 40 or 80Mhz, your network will still slow down to 20Mhz, and at the same time cause more interference due to constantly checking to see if it can use the larger widths). This problem also exists in the 5Ghz spectrum with the latest standards that support 80Ghz, there are effectively only 2 channels that will not overlap/interfere with each other.
I usually don't bother explaining 5Ghz much as when we are discussing dealing with a large home/area for coverage, 5Ghz just will not cut it due to the drastically higher interference it receives from objects/walls/humans due to less penetration capability of the frequencies. When trying to cover a large area, 2.4Ghz is what you need to use.
The final point that you really need to do is measure at each access point the strengths of the signals from the other access points that are nearby which use the same channel. Now with 3 channels in 2.4Ghz, you should be able to properly space a 4th or even more access points without having channel overlap (i.e. from any access point, you should not be able to detect the signal from another one on your network that uses the same channel). If you can detect a second one using the same channel, you need to tweak the transmit power of them so that they can no longer see each other. You should ideally also tune the transmit power across all the access points so that you have similar boundary cross-over/handoff ranges between all the access points (i.e. you want it so that the signal strength reaches low enough from the AP the client is currently using to reach the search threshold of the client to cause it to want to transition to a different AP, and ideally, you want that to happen before your client can see two APs that are using the same channel on your network).
But really, these above issues of tranmission power tuning only really crop up when dealing with installations that have more than 3 APs (or 2 in the case of attempting to have 5Ghz coverage).
The real issue with seamless transition is completely client based, and changing your WiFi access points to a "mesh" does not fix the issue. While you might see a fix, the reason for the fix is that you probably replaced/upgraded the client side device with hardware/software that now properly supports the transittion in the first place, which you could have done with your older network as well. The downside of the "mesh" is now you are using additional WiFi channels just to have the access points communicate back to each other, causing even more interference across your network than you would have had with wired access points.
I put that last bit in bold, as this is the real problem that people do not understand.
There is some other tuning that you can do when dealing with poor/bad designed clients that do not want to switch between access points, and that is to have a cutoff on the router for clients to be able to communicate using both the "minimum signal for authenticate" and "minimum signal for connection" values. Most all routers/access points default these to -128. By raising them to a higher value such as -60, the router/access point will prevent the client from connecting to it until it sees that as the minimum signal strength (you will need to tweak this based on the signal strength you scan across your coverage areas in the transition zones between the APs). Again, this can and may cause a hiccup for the clients that have bad tuning, but it will be better overall as a whole for your network since it forces them to switch to a different AP which will have better signal strength for servicing that client and will not cause the wifi network to drop down into degraded modes for all devices connected to it just so it can communicate to the worst signal devices on the network (as you are only as fast as the worst device on the channel).