There exist several LSTM variants, this may explain the difference you have observed.
{1} gives a list:
4.3. LSTM Variants
The vanilla LSTM from Section 2 is referred as Vanilla (V). The
derived eight variants of the V architecture are the following:
- No Input Gate (NIG)
- No Forget Gate (NFG)
- No Output Gate (NOG)
- No Input Activation Function (NIAF)
- No Output Activation Function (NOAF)
- No Peepholes (NP)
- Coupled Input and Forget Gate (CIFG)
- Full Gate Recurrence (FGR)
The first six variants are self-explanatory. The CIFG variant uses
only one gate for gating both the input and the cell recurrent
self-connection (an LSTM modification proposed in GRU (Cho et al.,
2014)). This is equivalent to setting $f_t = 1 − i_t$ instead of
learning the forget gate weights independently. The FGR variant adds
recurrent connections between all the gates as in the original
formulation of the LSTM (Hochreiter & Schmidhuber, 1997). It adds nine
additional recurrent weight matrices, thus significantly increasing
the number of parameters.
References: