Not necessarily. Rules vary from place to place depending on legacy dialing procedures and contemporary needs. Some places need to dial only seven digits even when crossing an area code boundary. Other places must dial ten digits even within their own area code. It's very complicated.
I believe today's system is set up so that you can dial 1+area code+7digits regardless of where you're calling and if the area code is needed or not.
My region, for example, has 10 digit dialing. If I call a different area code (overlay or adjacent) within my region, whether it is a toll call or not, I do not need the "1". If I go outside the region I do need the 1.
There's a artificially defined border known as the LATA, which separates local from toll calls; that is, calls handled by the local telephone company vs. calls handled by a "long distance" company. Anyway, some area codes span multiple LATAs. That is, one can dial only seven digits yet be charged for a long distance call. Other area codes are very small or even overlays for the same region.
The above mess is a result of (1) divesture of long distance from the once central Bell System, and (2) competition in local phone service resulting in an explosion of exchanges which in turn required many new area codes.
In the old days, the "1" was not universal. Area codes originally had a middle digit of only 1 or 0 and exchanges did not have a 1 or 0 as the middle digit. By this standard the switchgear could distinguish the type of call.
The "1" prefix was used for two reasons: 1) to serve as a toll alert. In my area, making a toll call within the same area code required a 1, that is, 1+7 digits. 2) To serve as a long distance signal to the switchgear. While the switchgear didn't actually need the 1, having it made circuitry simpler for some exchanges. (Some places used other codes). As mentioned, not all places required the 1, you just dialed the ten digits.
There is also the 0 prefix (0+ac+7d) which is used to signify operator assistance, such as for collect, 3rd party billing, person to person, time and charges, credit card.
The concept of a "toll alert" is somewhat obsolete because of the great variety of billing plans. I have national unlimited, so theorectically I don't need the 1 at all. But obviously some people have a la carte plans.