Garden plants cannot distinguish between the nutrients supplied in fertilizers applied in the landscape, regardless of what the product name suggests. The amount of nutrients, which varies in formulations among fertilizers, does result in different effects, however.
Lawn fertilizers typically are richly abundant in nitrogen and quite lean in other nutrients like potassium and phosphorus. Nitrogen in the soil allows plants to grow new stems and leaves, which is ideal for a lush green lawn but not ideal for other plants in a diverse garden.
All garden plants utilize the nitrogen supplied in lawn fertilizers, but the large amounts of nitrogen in lawn fertilizer formulas isn't ideal for nongrass plants. Applying too much nitrogen in the garden causes plants to increase growth rates and produce lots of leaves. The lack of certain nutrients in the lawn fertilizer causes the explosion of leafy growth to falter or become weak. Excessive nitrogen also doesn't promote flower production in the garden -- undesirable in an ornamental landscape.
As long as the lawn fertilizer doesn't contain a pesticide or herbicide chemical that would harm other garden plants, the fertilizer may be used. To prevent application of too much nitrogen, scatter the fertilizer at one-fifth or one-fourth the rate. Apply another fertilizer that supplies other nutrients to create a well-balanced nutrient application.
Some plant types in general do not respond well to high dosages of nitrogen. According to Learn2Grow, conifer evergreens don't typically respond well to excessive nitrogen applications, for example.