What type of chemical bond makes the alloy steel?

In a metal, each metal atom is conceived to donate a few of its valence electrons to the lattice, such that metal nuclei acquire a positive charge. This non-localized metallic bonding is believed to be responsible for the general properties of a metal: malleability, ductility, conductivity to heat and electricity. The alkali metals, lithium, sodium, potassium, rubidium, have only the 1 electron to contribute to the metallic lattice. Alkali metals thus tend to be soft, and low melting. Many electron metals, such as iron, have higher melting points, but do retain malleability and ductility at elevated temperatures.

So, steel is a metal, and as such displays metallic bonding. What makes steel steel is the addition of a little carbon during its manufacture (up to 1-2% w/w). Steel is thus an alloy of iron and carbon, and is the premier material for tools.

How the carbon is bound to the iron atoms, is beyond me, and it is an area where chemistry turns into metallurgy, where end use and function takes a higher precedence than chemistry. Many other metals are present in steel, and the various alloys may be tailor-made for a specific purpose.