Do I understand correctly that the typical way to draw multiple objects that each have a different texture in OpenGL is to simply bind one texture at a time using glBindTexture and draw the objects that use it, then bind a different texture and do the same?
In other words, only one texture can be "active" for drawing at any particular time, and that is the last texture that was bound using glBindTexture. Is this correct?
bind one texture at a time using glBindTexture and draw the objects that use it, then bind a different texture and do the same?
In other words, only one texture can be "active" for drawing at any particular time
These two statements are not the same thing.
A single rendering operation can only use a single set of textures at any time. This set is defined by the textures currently bound to the various texture image units. The number of texture image units available is queryable through GL_MAX_COMBINED_TEXTURE_IMAGE_UNITS.
So multiple textures can be "active" for a single rendering command.
However, that's not the same thing as binding a bunch of textures and then rendering several objects, where each object only uses some (or one, in your case) of the bound textures. You could do that, but really, there's not much point.
The association between a GLSL sampler and a texture image unit is part of the program object state. It's the value you set on the sampler uniform. Therefore, in order to do what you suggest, you would have to bind a bunch of textures, set the uniform to one of them, render, then set the uniform to the next, render, etc.
You are still incurring all of the cost of binding those textures. You're still incurring all of the overhead of changing uniforms. Indeed, it might be less efficient, since the normal way (bind, render, bind, render) doesn't involve changing uniform state.
Plus, it's just weird. Generally, you shouldn't be changing uniform sampler state dynamically. You define a simple convention (diffuse texture comes from unit 0, specular from unit 1, etc), and you stick to that convention. Any GL 3.x-class hardware is required to provide no less than 48 texture image units (16 per stage), so it's not like you're going to run out.
There are mechanisms to do things not entirely unlike what you're talking about. For example, array textures can be leveraged, though this requires explicit shader logic and support. That would almost certainly be faster than the "bind a bunch of textures" method, since you're only binding one. Also, the uniform you'd be changing is a regular data uniform rather than a sampler uniform, which is likely to be faster.
With the array texture mechanism, you can also leverage instancing, assuming you're rendering the same object with slightly different parameters.