Shares are a form of equity. Owning the shares will give you a claim to the residual assets of the company after all the liabilities have been settled. So what you own is effectively the 'Net Assets' of the company. This is different from outright owning the actual underlying assets of the company.

To slightly complicate things, the total assets shown on the annual report of these companies are mostly on their cost basis. During an acquisition like this, they would be 'fair valued', which could result in significant write up or write off compared to the cost basis.

Market capitalization is the value of all the public shares, and is determined by investor sentiment about the medium/long-term prospects of the company as much as any other factor. The underlying assets are wholly owned by the company and have an intrinsic value that is easier to measure through accounting, but that alone doesn't take in to account the liabilities or debts on the books.