The accurate classification of seizure types using electroencephalography (EEG) signals plays a vital role in determining a precise treatment plan and therapy for epilepsy patients. Among the available deep network models, Convolutional Neural Networks (CNNs) are the most widely adopted models for learning and representing EEG signals. However, typical CNNs have high computational complexity, leading to overfitting problems. This paper proposes the design of two effective, lightweight deep network models; the 1D multiscale neural network (1D-MSCNet) model and the Long Short-term Memory (LSTM)-based compact CNN (EEG-LSTMNet) model. The 1D-MSCNet model comprises three modules: a spectral–temporal convolution module, a spatial convolution module, and a classification module. It extracts features from input EEG trials at multiple frequency/time ranges, identifying relationships between the spatial distribution of their channels. The EEG-LSTMNet model includes three convolutional layers, namely temporal, depthwise, and separable layers, a single LSTM layer, and two fully connected classification layers to extract discriminative EEG feature representations. Both models have been applied to the same EEG trials collected from the Temple University Hospital (TUH) database. Results revealed F1-score values of 96.9% and 98.4% for the 1D-MSCNet and EEG-LSTMNet, respectively. Based on the demonstrated outcomes, both models outperform related state-of-the-art methods due to their architectures’ adoption of 1D modules and layers that reduce the computational effort needed, solve the overfitting problem, and enhance classification efficiency. Hence, both models could be valuable additions for neurologists to help them decide upon precise treatments and drugs for patients depending on their type of seizure.