The all-in-one inverter/charger units will often have features missing from separate components.
For instance, some can be configured to not draw above a certain amount from shore power. Useful if you're plugged into say a 15a shore plug and are worried about popping the shore breaker.
Another feature that some inverter/chargers have is the ability to momentarily pull power from the battery to augment the incoming shore power to service momentary high loads, such as air conditioning compressor startup.
With separate components, the inverter is generally direct to battery full-time and the electrical outlets fed from the inverter full-time. A standalone inverter has no provision to accept input from shore power. The shore power simply feeds the battery charger and no transfer switch is needed.
In such a system, the transfer switch is usually only needed to switch between shore power or generator to feed the battery charger.
Of course, you can always add complexity. You could use a transfer switch to feed the electrical outlets from either shore power or inverter and hard-wire the battery charger to shore power.
You would still need another transfer switch if you wanted to switch between shore power and on-board generator to power the battery charger and electrical outlets.