Does higher stock price mean that the company is worth more?

Not at all. Market capitalisation is a function of two things:

Market Capitalisation: Share price x Number of shares outstanding.

That said, market cap is not to be confused with valuation (often a loosely held term).

To take it one step further from an equity analyst's perspective, look at Total Enterprise Value, which is the sum of Equity plus Debt.
TEV = Assets = Equity + Debt.
Eg. If Market Cap is $5 billion and you have another $1 billion of debt on the books, then your TEV = $6 billion.
As such, it's often a good idea to clarify what people are referring to when they ask for valuation. Is it merely market Capitalisation, or Total Enterprise Value (TEV).

Hi there!

Not necessaily. This depends on the market capitalisation!

For instance, stock A costs $100 per share and has 10 shares outstanding, its market capitalisation would be $1000

In another case, stock B costs $10 per share and has 1000 shares outstanding, its market capitalisation would be $10,000.

It is important to look at both price and number of shares outstanding to determine the market value of a company!