Some Comments
If I may:
-- A relay is nothing but a remote control switch. It does not charge anything, it merely makes or breaks a circuit. A relay can be controlled by a switch or some form of automatic controller. A relay needs to be heavy enough to carry the maximum current in a circuit without failing.
-- A voltage sensing relay is one that opens and closes in response to the voltage passing through the relay. Most sense the voltage on either side of the relay, but you could design one that reads only one side. Most incorporate some additional intelligence such as a time delay to reduce the chances of the relay opening or closing too soon or too often.
-- In a typical battery charging scenario for a 12v circuit the relay will close (make contact) when it detects 13v or more. The exact voltage may be adjustable and, as noted, there may be a time delay to assure that the voltage is stable at 13v or more. If the relay detects that the voltage has dropped to 12.7v, then the relay will open. 12.7v is the typical "full charge" voltage for a "12 volt" battery. Again, some models are adjustable. The Australians, for example, sell some with a "winch mode" which is intended to stay connected even when the voltage drops to 12.5v under the load of a winch. (I think a dash switch is a better idea.) The relay may also incorporate catastrophic high and low voltage cutouts - typically over 16v or below 11v.
-- The batteries within a given battery bank, that is batteries that are permanently connected together, whether in series or parallel, when both charging and discharging, should match exactly. Even to sequential serial numbers if you can arrange it.
-- Batteries that are only connected when under charge, as for example a typical set up on a yacht, RV, or narrowboat do not have to match in size. In fact, they will almost never match in size. In a properly designed system, for example one controlled by the ignition switch or by an intelligent voltage sensing relay, there is no need to worry about a size imbalance because as soon as the ignition key is "off" or as soon as either battery drops back to a "full" charge, the relay will open keeping the batteries isolated from each other.
-- Batteries and their chargers do have to match. Typically, a deep cycle AGM battery (e.g. Lifeline) calls for a charge voltage of 14.4v at 20C/70F. An open cell deep cycle battery (e.g. Trojan) calls for around 14.8v. This means that if you are going to use a relay based system, then your camper/house battery should have have grossly the same voltage requirements as you starter battery, or, more properly, the output of your vehicle's alternator/regulator combination. If they do not match, then you will need to compensate.
-- Many modern vehicles come from the factory with some form of AGM battery and easily produce the required 14.4v. (The exact voltage should vary with temperature.) There are some exceptions - many Toyotas only produce 13.9v and some Sprinters will reach, but not remain at 14v+. In this case you may have problems with a relay based system.
-- There are several options if your vehicle cannot produce the required voltage:
1) Raise the alternator to the desired level. In many cases this is easily done through an aftermarket adjustor by by replacing a diode. (The latter trick being popular in Australia with Toyotas.) This is what Expo member "skygear" does with his Toyota.
2) Use a Battery to Battery charger such as made by Sterling Power or CTEK. This allows you to run a different charging voltage to each battery bank.
3) Make up the difference with a solar or shore charger. Obviously, your charge will be slower if your alternator is putting out 13.9v as opposed to 14.4v, but if your solar charger is putting out a full 14.4v you will still achieve a complete charge.
CTEK, for example sells two components, the D250S and the SmartPass which are designed to work together. When the camper battery is deeply discharged, the system closes a relay rated at 80A to allow direct connection between the starter and camper batteries. As the camper battery charges and the charge rate drops to 20A, then the relay opens and the battery to battery charger finishes the charge, boosting the charge voltage to the desired level. (The unit also includes a small solar controller.)
Some final notes:
-- All charging systems require properly sized wiring to assure a fast charge. If the wiring is too small, then the transfer of current will be very slow, leading to the old camper's tale: "You can't charge your camper battery from the engine." Yes, you can, but it may take forever. Once you get into the 1 AWG range, voltage drop becomes less and less of an issue, because as the charge rate drops, the voltage drop reduces as well. Thus you can design a very effective system that appears to be slightly undersized.
-- Lead Acid batteries require a long, long absorb cycle. Much longer than most of us will ever drive during a given day, thus most of the worry about a true float is irrelevant when charging from the engine. A greater need is solar or shore power to complete the charge.
-- Lithium is different.