No, not generally. But there are practical reasons for doctors to think that way. In the first 13 weeks, the fetus is likely to damaged by certain medications, etc. After 13 weeks, spontaneous miscarriages are far less likely. Some women think it's alright to smoke and drink alcohol in the second trimester.
At 26 weeks, the fetus is generally viable; and 39+ weeks is term. These days, though, some 20 week babies survive.
There are also differences between 1st, 2nd and 3rd trimester terminations.
But generally, women in the West count by weeks.