Peter Thaarup Hoegh, 59, mayor of this largest town in Greenland, and Henriette Rasmussen, 28, a school teacher here, are both going to vote no tommorrow when almost 38,000 Greenlanders cast ballots in a referendum that is expected to result in home rule within the Danish kingdom for huge, icy but strategically located island.

These two native Greenlanders, however, are voting no for quite different reasons, and those differences reflect an important gap in generations and attitudes that eventually could take the people of Greenland on a course toward total independence rather than just home rule.

The home rule referendum, developed jointly by a commission of Danes and Greenlanders, will give Greenland far more self-government and control over vital decisions than it has had in the past as a state of Demmark, while keeping the island within the Danish nation and under Copenhagen's constitution.

The referendum is certain to be approved, possibly by a 2-to-1 majority.

Mayor Hoegh, however, says he is satisfied with the existing situation and is uncertain about developments moving too fast on an island that has a primitive economy, few skilled workers and only about three years of experience in the simplest from of self-government at municipal levels.

Even the three island-wide political parties are only a few years old.

So, even though home rule will be a gradual thing beginning next May, and with Danish economic and technical support continuing indefinitely, Hoegh and probably a few thousand other older Greenlanders are not especially confident.

Rasmussen's vote may b e more significant, because it reflects a trend among an uncertain number of young people in a region where more than half the island's native population is 18 or under.

Home rule, she acknowledges, will increase political awareness among Greenlanders isolated from the rest of the modern world for all but the last few decades. Because of that, she is optimistic about the island's future.

"But most young people here want independence," she said.

As for the predominant argument that Greenland could not support itself without continued heavy Danish subsidies for modernizing the region, she says, "We have different ideas of what this country should be. We have a survival instinct from our Eskimo ancestors. We don't need the Danish electrical system and toilet system and this hotel," she said, sitting in the lobby of a modern new hotel here. "This is not part of me."

So, she says, "I want to be among those who are going to create something new as the next step."

Rasmussen is not a political party member. But Ivalu Egede, 22, is press representative for a new socialist youth party that sprang up here three years ago and is estimated to have anywhere between 1,000 and 5,000 followers.

Her Inuit Ataqatigiit Party, which she says includes members "who take a Marxist view of history." not only favors complete independence but also rejects numerous provisions of the home rule bill as intended to continue Danish dominance, including a controversial compromise on what happens if oil or other major mineral wealth is discovered in the vast Arctic island.

Measuring political attitudes in this island, especially for outsiders, is extremely difficult. Communications are primitive. The Greenlanders are strung out in mostly small settlements along the coast of a 1,650-mile long island whose center is frozen into a permanent mountainous ice sheet.

News is carried primarily by short-wave radio. Weekly newspapers sometimes take three months to reach northern settlements. The island's fledgling TV station here was off the air, as far as local programming was concerned, for four months before the referendum because of technical problems.

Nevertheless, several young and educated native Greenlanders interviewed generally expressed the view that many young people here do favor independence, some sooner, some later.

Assessing relations between the native Greenlanders and the 8,000 or so Danes that live and work here, and between Copenhagen and Godthab, is also difficult and complex.

The two areas have a 250-year association.Greenland was first a Danish colony and then, in 1950, became a Danish state.

There are many intermingled families and undoubtedly warmth between many individual Danes and Greenlanders. But there are also problems and animosities. Very few Danes really speak Greenlandic.

"So you never really know what's on their mind," says a Danish doctor here.

For the majority of Greenlanders, however, the view of home rule is positive.

"We say yes to home rule," says Lars Chemnitz, of the Atassut Party, "Because it is a unique offer, the fruit of positive cooperation between the old colony Greenland, and Denmark. It is an example of a sound and continuing development between the two."

The Atassut Party, generally conservative in outlook, is one of the two major political parties here along with the slightly larger Siumut Party, whose leaders describe it as slightly left of a typical Social Democratic Party in Western Europe.

Chemnitz and Siumut spokesman Lars Emil Johansen, both of whom are native Greenlanders, despite their European-sounding names, both reject independence for Greenland not only on economic grounds but because it would be "impossible and unrealistic" for a country so vast yet with such a tiny population to defend itself, to keep from becoming caught up in the great power struggle and to isolate itself from the outside world.

Retaining the relationship with Denmark enables Greenland, where the United States still retains a