Multiword Terms (MWTs) are domain-specific Multiword Expressions (MWE) where two or more lexemes converge to form a new unit of meaning. The task of processing MWTs is crucial in many Natural Language Processing (NLP) applications, including Machine Translation (MT) and terminology extraction. However, the automatic detection of those terms is a difficult task and more research is still required to give more insightful and useful results in this field. In this study, we seek to fill this gap using state-of-the-art transformer models. We evaluate both BERT like discriminative transformer models and generative pre-trained transformer (GPT) models on this task, and we show that discriminative models perform better than current GPT models in multi-word terms identification task in flower and plant names in English and Spanish languages. Best discriminate models perform 94.3127%, 82.1733% F1 scores in English and Spanish data, respectively while ChatGPT could only perform 63.3183% and 47.7925% respectively.