There are different kinds of frames. A common frame to use is a coordinate frame. For that all you need to imagine is each region of spacetime has a coordinate system that you can use in that region to find and label all the events in that region.
An advantage to this is that you can practice using arbitrary coordinate systems even while still doing Special Relativity, just do Special Relativity in polar coordinates, then in cylindrical coordinates, then in spherical coordinates, etcetera. Learn how to use all these different coordinates system, but don't (yet) worry about curvature or General Relativity. Same things with tensors, you can learn to use them in Special Relativity.
Your textbook does these things actually. So maybe your confusion is that you think the General Relativity section has started before it has actually started, or maybe you skipped ahead.
Now, however, there is a completely different way people use the word frame, which is to refer to a frame of vectors. In that case each event has some vectors, enough to specify all the velocities and such at that point. This is very different, because these vectors give you directions but they do not give you coordinates. In a Euclidean space they might look like the exact same thing (in a Euclidean space, vectors and covectors also look the same, but they are different), so let's tell the difference.
I will set up a polar coordinate system to explain the difference. In polar coordinates you can move outwards one radial coordinate (so one meter out), then over one angular coordinate (so one radian over), then back in one radial coordinate system (so one meter in) then back over one angular coordinate (so one radian back). You end up back exactly where you started. Coordinates locally look like distorted graph paper, they always have that property.
But what if you had a frame of vectors that everywhere had a vector pointing radially outwards and another one pointed in the clockwise direction? If you moved one meter outwards, then one meter counterclockwise, then one meter radially inwards, then one meter clockwise then ended up moving clockwise. So a coordinate system and a frame of vectors are different.
Coordinate systems are something you'll have to learn to deal with, and how to do calculus in them. And even in Special Relativity, you can have a metric that varies from place to place in your coordinate system. The polar, cylindrical, and spherical coordinate systems are examples of that.
Later on, you'll also have to deal with curved coordinate systems, which means the metric must vary from place to place, but it will do so in particular in a way that affects parallel transport. Thus geodesics can converge, which will be how massive bodies exert tidal forces.
You can't measure distances between events with a coordinate system alone. But if you already have a coordinate system can do it if you also have a metric. But if you want to move around you can completely describe your motions by saying how the coordinates change. It helps to be an expert in describing changes through changes in coordinates, because then you can describe the metric in terms of how actual metric distances are related to coordinate distances. So you can use coordinate distances as a foundation to build upon. And again, doing it for interesting coordinate systems in the context of regular euclidean geometry or in regular Special Relativity is a good practice and you should consider it and your textbook does it, so your textbook is assuming you have that facility.
So now let's get to a frame of reference. A frame of reference is definitely a coordinate system. However if you want to bring in clocks and rulers they measure actual distances, so they will have a nontrivial relationship to your coordinates, and the metric will tell you exactly how they are related.
Maybe by frame of reference you mean a coordinate system with a metric. Having them both. An inertial reference frame is a special frame, one where the coordinates represent the motions of test particles subject to no external forces. These strictly only exist locally.