They are not the same.
Basic accounting equation:
Assets = Liability + Shareholder Equity
Assets refers to what the company actually owns: cash, property, inventory, etc.
Assets are paid for in two major ways: debt (liability) and stock (equity). Essentially, everything a company owns is paid for by a combination of (1) getting loans from other entities or issuing bonds and (2) having other entities own a part of the company.
Equity includes a number of things, but the most common form is stock, or ownership of a company.
An example of this: if you own a pen company, assets might include pens, and equity would be your ownership of the company.