Based on the articles I have read, spatial ecology and landscape ecology are similar but quite different. Landscape ecology focuses on understanding how populations and communities respond to changes in land use and cover (Mimet et al. 2016). On the other hand, spatial ecology focuses on a wider range. These would include effects of global changes--such as climate and altered biogeochemical cycles and disturbances--on spatial or temporal scales (Laffan et al. 2016). Both landscape and spatial ecology concern themselves over environmental management decisions and how biodiversity can be affected.
Here are some articles in case you're interested to read more:
Mimet A, Pellissier V, Houet T, Julliard R,
Simon L (2016) A Holistic Landscape Description
Reveals That Landscape Configuration Changes
More over Time than Composition: Implications for
Landscape Ecology Studies. PLoS ONE 11(3):
e0150111. doi:10.1371/journal.pone.0150111
Spatial Ecology : Patterns and Processes by Rai, Vikas Bentham Science Publishers. 2013
Shawn William Laffan, Andrew K. Skidmore & Janet Franklin (2016)
Space, time, connectivity and conflict in biological landscapes: the fourth special issue on
spatial ecology, International Journal of Geographical Information Science, 30:1, 1-4, DOI:
10.1080/13658816.2015.1090001
Landscape Ecology for Sustainable Environment and Culture