Here's a nice article about plant nutrients:
Plants need NPK and a lot of other nutrients. Nitrogen is basic plant food and helps grow big leafy plants. Phosporus is needed for good root growth and blooming. Potassium helps with water regulation and other processes and is needed for fruiting.
So lawn fertilizers are almost all N, because all you are growing is leaves (the blades of grass are its leaves). For growing roses, etc fertilizers tend to be high in P for the blooming. For growing tomatoes, you need a lot of P and K. Too much N and you get big leafy plants at the expense of flowering and fruiting.
But synthetic fertilizers only provide the NPK and none of the other nutrients and not in the best form for plants to use. Too much of one nutrient, can lock up the others in the soil, making them unavailable. So yes you can easily overdo the NPK and either burn or starve your plants.
Plants need all the nutrients and they need a whole range of soil life and micro-organisms to break the nutrients down in to a form they can use it.
What you want is compost and/or a good organic fertilizer with all the trace nutrients and micro-organisms.