Narrow-line Seyfert 1 galaxies (NLS1s) are believed to be active galactic nuclei (AGN) in the early stages of their evolution. Several dozen of them have been found to host relativistic jets, whilst the majority of NLS1s have not even been detected in radio, emphasising the heterogeneity of the class in this band. In this paper, our aim is to determine the predominant source of radio emission in a sample of 44 NLS1s, selected based on their extended kiloparsec-scale radio morphologies at 5.2 GHz. We accomplish this by analysing their spatially resolved radio spectral index maps, centred at 5.2 GHz, as the spectral index carries information about the production mechanisms of the emission. In addition, we utilise several diagnostics based on mid-infrared emission to estimate the star formation activity of their host galaxies. These data are complemented by archival data to draw a more complete picture of each source. We find an extraordinary diversity among our sample. Approximately equal fractions (∼10–12 sources) of our sources can be identified as AGN-dominated, composite, and host-dominated. Among the AGN-dominated sources are a few NLS1s with very extended jets, reaching distances of tens of kiloparsecs from the nucleus. One of these, J0814+5609, hosts the most extended jets found in an NLS1 so far. We also identify five NLS1s that could be classified as compact steep-spectrum sources. In addition, one source shows a possible kiloparsec-scale relic that reaches well outside the host galaxy as well as restarted nuclear activity, and one could belong to the sub-class of NLS1s that host relativistic jets that seem to be absorbed at lower radio frequencies (< 10 GHz). We further conclude that, due to the variety seen in NLS1s, simple proxies, such as the star formation diagnostics also employed in this paper and the radio loudness parameter, are not ideal tools for characterising NLS1s. We emphasise the necessity of examining NLS1s as individuals instead of making assumptions based on their classification. When these issues are properly taken into account, NLS1s offer an exceptional environment for studying the interplay between the host galaxy and several AGN-related phenomena, such as jets and outflows.