Hi cmorris,
A bed frame is part that supports the foundation and holds it up off the floor and can either be a steel frame like you have or a wooden bedframe. Both of them need good support with a midbeam and legs to the floor on each side and in the middle of the frame (preferably two legs in the middle) … especially with larger sizes such as queen and king size to prevent sagging in the middle. Some wooden bedframes are designed to use with a foundation either for even support without gaps that the mattress can sag into under the mattress or for extra height and some like platform beds have more closely spaced slats across the surface so a foundation isn’t necessary for even support and a mattress can go directly on the slats (although you can still use a foundation if you want the extra height).
A box spring is usually used with innerspring mattresses that are designed to use them and have springs inside them. A foundation has no springs inside and is either a slatted or solid rigid surface. There is more about foundations and box springs in the first post of this thread and the posts it links to in the second paragraph.
Your current steel bedframe will probably be alright as long as it is the right size and has good support to the floor under the midbeam. Three legs on each side would be stronger than two and and two or three legs under the midbeam would be stronger than one.
So you need something to raise your entire sleeping system up off the floor (the bedframe), then a foundation or a suitable slatted surface to evenly support the mattress and then the mattress itself goes on top of this.
Phoenix