The forcing 1NT convention, is popular because it may be used to show hands with intermediate strength, but lack three card support for the major opening. However, the semi-forcing 1NT convention is becoming more popular.
What is the difference?
The primary difference is that the opener may pass the bid of 1NT with a balanced hand.
Let’s consider an example.
Opener’s Hand 
KJ5 
AT752 
Q4 
K98
Responder’s Hand Q93 J3 J972 AT32
Playing a standard forcing 1NT bid, the bidding would be: 1-pass-1NT-pass-2-pass-2-pass
However, playing 1NT as only semi-forcing, because the opener has a balanced hand, he may pass. Clearly, the contract of 1NT is the superior contract.
As another example, consider the hand:
Opener’s Hand QJ82 AK754 J7 K4
Responder’s Hand T64 9 KQ92 QJ863
Playing the 1NT forcing system, one would again bid 2 which responder will pass. Again, one sees that the semi-forcing convention is superior since one would play the hand in 1NT. Before replacing the 1NT forcing convention with the semi-forcing convention, one should consider the risks.
In 2/1, if one has three card support for the major and 10-12 HCP, one bids 1NT (5-12 HCP) and then jumps to three of the major.
Using the semi-forcing convention, 1NT must be redefined as 6-10 HCP with no support for the major opening. With support, the limit raise in the major must be re-defined as 3+ card support for the major opening and you cannot play Bergen raises.
If you do not play Bergen raises and use the double jump in the major as a limit raise with four card support, one should consider replacing the forcing notrump convention with the semi-forcing convention with the limit raise re-defined as 3+ support since it gives up nothing and may more easily allows you to bid some awkward hands.
Discuss the change with your partner! Note, if you play Standard American or the SAYC, the 1NT bid is always semi-forcing and defined as 6-9 HCP with less that three card support for the major.