For much of the past decade, investing abroad didn't pay off for U.S. investors as technology stocks powered domestic markets. Now with the S&P 500 lagging behind international markets for the second consecutive year and concerns about the benchmark's heavy tech concentration, overseas stocks have returned to favor.

But investors who want to diversify their portfolios by adding international-stock funds may unwittingly be doubling down on U.S. stocks instead. That is because although stock index funds with names such as "international," "world" or "global" do provide exposure to foreign stocks, some may own U.S. stocks as well-up to 60% or more in some cases.

"It's important [investors] do some due diligence in terms of the 'how is the index constructed' and what it includes so that they understand what they're actually getting," says Catherine Yoshimoto, director of product management at FTSE Russell.

Consider two popular Vanguard exchange-traded funds that show how the change of one word-world instead of international-changes the funds' makeup: the $98 billion Vanguard Total World Stock ETF $(VT)$ and the $161 billion Vanguard Total International Stock ETF $(VXUS)$.

The world fund has a 62% weight to the U.S. and a one-year return of 24%. Nine of the top 10 holdings of the world fund are identical to Vanguard S&P 500 ETF $(VOO)$, with the difference being the Vanguard world fund has Taiwan Semiconductor Manufacturing in its top 10 versus JPMorgan Chase in the S&P 500 fund.

The international fund has no U.S. exposure, with Japan its largest country weighting at 15%, and a one-year return of 27%.

The methodology behind the madness

So how does a fund labeled world end up with such a heavy dose of U.S. stocks?

The reason comes down to the definitions institutional investors use. Historically, "international" investing meant owning developed markets outside the U.S. As emerging markets began to open to foreign investors, index providers built broader benchmarks-often labeled "world," "global" or a similar variation-that combined developed and emerging markets, and unlike "international" indexes, could include the U.S.

These terms drive returns, says Aniket Ullal, head of ETF research and analytics at CFRA Research, as ETF and mutual-fund providers use the indexes to create the funds.

Yet there is no standard industry definitions nor regulations for those broad terms when it comes to naming the fund, says Kathy Kellert, head of equity index product at Vanguard, leaving it up to the issuer to determine what name is clearest or will resonate with investors.

Index providers such as MSCI, FTSE Russell and S&P Dow Jones use a mix of common and proprietary quantitative and qualitative data-such as economic development, and the size and liquidity of the country's markets-to classify countries into developed and emerging markets.

It is why the world and global funds that include U.S. stocks will look similar to U.S. funds like the S&P 500. MSCI, for instance, defines "world" as developed markets only, so without including emerging markets to counterbalance some of the U.S. stock influence, the percentage overlap with the S&P 500 rises.

How much room a country occupies in the index changes over time, depending on the strength of its economy and companies, said Raman Aylur Subramanian, head of market classification taxonomies at MSCI.

Depending on the index provider, the U.S. now accounts for between 60% to 65% of the global market capitalization. This isn't an intention to mislead, but rather reflective of the U.S. market's liquidity and American companies' profitability.

What in the world?

How, then, should do-it-yourself investors who already have substantial U.S. holdings proceed?

Ullal suggests looking for funds labeled international rather than global or world funds, unless those world and global funds specify these exclude the U.S. Examples of funds without U.S. exposure include the $11.8 billion iShares MSCI ACWI ex-U.S. $(ACWX)$ or the aforementioned Vanguard Total International Stock ETF.

Ullal says investors might also consider splitting exposure into international developed and emerging-markets funds for both geographic and sector diversification.

Such funds include the $315 billion Vanguard FTSE Developed Markets Index Fund ETF $(VEA)$ or the $193 billion iShares Core MSCI EAFE ETF (IEFA). Complementary emerging-market funds from those issuers are $162 billion Vanguard FTSE Emerging Markets $(VWO)$ or $154.6 billion iShares Core Emerging Markets ETF $(IEMG)$.

Investors also should check that the name of the fund and the underlying benchmark align with their expectations. An example is the $8.4 billion iShares MSCI World ETF $(URTH)$. The iShares fund uses the MSCI World Index and its top 10 is identical to the S&P 500, with 26% of its 1,281 holdings in the top 10, and the U.S. comprises 72% of the fund. The iShares fund has 22% one-year return.

In the aforementioned Vanguard Total World Stock ETF, the word "total" is a buyer's first clue that it is more than just developed-market large and midcap companies. That fund tracks the performance of FTSE Global All Cap Index, which measures the performance of large, midcap and small-cap companies around the world. That is why the holdings and returns are different from the iShares world fund.

Because of the nuances between indexes and how fund issuers define and disclose what's in the fund, DIY investors may want to avoid a lot of mixing and matching of funds from different issuers, says Neale Ellis, co-chief investment officer at Fidelis Capital. "You may end up doubling up or not getting anything if you're not operating from the same definition," he says.

Write to reports@wsj.com