Commands such as “close”, “side”, “heel” are all intended to communicate to the dog how much freedom of movement they have (whether or not they are also on a leash).
“heel” is a command traditionally used to ask the dog to align themselves with the handler’s left side with their shoulder exactly even with the handler’s left leg - no matter how the handler moves in direction or pace.
“side” is traditionally used to align the dog to the handler’s right side.
“close” is traditionally used to describe a “loose leash” position relative to the handler. With most handler’s envisioning the dog on a 6 foot lead - this allows the dog more range of movement than a formal heel or side, but within a limited radius (again whether they are on leash or not).
Every puppy training class will cover ways to train these behaviors via luring, targeting, capturing, perch work etc... so I won’t belabor the point here - just that it is very helpful for both response to handling cues and setting up training exercises to have the ability to orient your dog to both sides and to be able to walk with them with some measure of control, even if not formal obedience heel work.