The House is about to move from the world of Bill Gray to the world of Jamie Whitten. The distance is, among many other things, both generational and institutional. Mr. Gray, who was two months old when Mr. Whitten was first elected to Congress in 1941, has risen in four terms to be chairman of the Budget Committee. Mr. Whitten is chairman of Appropriations. Budget is the new committee that sets broad fiscal policy and gets the headlines, but old-line Appropriations remains the one that controls the details.

Mr. Gray has now largely done his work for the year (and well). A conference committee is trying to reconcile the budget resolutions that Senate and House passed last month. The work has been difficult, particularly on defense and taxes, and it is not clear what result will be reached before Congress begins its July 4 recess this weekend. But in most domestic areas House and Senate are not far apart.

The budget resolution is followed each year by implementing legislation, including the traditional appropriations bill. Partly for fear of running out of time, Mr. Whitten's subcommittees have begun work on these. The new budget process that Congress set up along with the budget committees in 1974 took away some of Appropriations' autonomy. Thus the House-passed budget resolution limits the funds available to Appropriations for next fiscal year, and means that most if not all the subcommittees will have to vote cuts. The new Gramm-Rudman rules may impose further constraints.

But a great deal of power remains with Appropriations, the more so because the details of which it is master tend to blur and are not so well publicized, leaving it a freer hand. In last year's budget resolution, for example, the conferees left funds so that hardly any cuts would have to be made in programs for the poor. But a new study by the Center on Budget and Policy Priorities shows that the Appropriations committees then "departed from the assumptions of the budget resolution" and shifted these funds around, cutting programs for the poor by about $1 billion. Will they do so again?

The appropriations bills are also where aides say the president plans to apply veto pressure this year (as he also did last). The budget resolution remains enormously important. It is the instrument through which Congress has leveled off the defense buildup the last two years, and through which it is pressing the president to raise taxes. But the appropriators have the keys to the Treasury.