Here's the basic history of character forms.
Oracle bone script
Chinese bronze inscriptions
Traditional Chinese characters
Simplified Chinese characters
The above are about Chinese script's history. A “script” is a system/style of writing. Script is not about font/typeface. Font and typeface are related to printing.
Also note, there are 2 distinct concepts:
For example, both traditional/simplified Chinese characters can be written in several styles. ⁖ cursive, regular. And a subset of the characters exist in Bronze Script (甲骨文) or Seal Script (金文).
Though, the 2 concepts are tied together. For example, Oracle Bone Script and Bronze Script are both about style and about actual character forms.
For detail, see: What are Chinese serif and sans-selif Font Names.
For font comparison, see: Chinese Fonts Comparison; 中文字體比較.