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There really is no difference.
I will say though that often times a garden center or nursery will reference a bush as smaller with leaves that touch the ground. A shrub may be a bit taller specimen.

https://www.gardeningknowhow.com/ornamental/shrubs/spirea/growing-spirea-shrubs.htm

Whenever possible transplant your Spirea in the late winer or early spring before the new growth begins.

If they need to be moved after they have begin growing, you can prune back the plant by 1/3 to help with transplant shock.

Water the plant well in the 48 hours before digging and moving and make sure you provide plenty of water to the shrubs after moving.
Place them in the new planting hole at the same depth.

Spirea will tolerare clay soil conditions.

https://www.gardeningknowhow.com/ornamental/shrubs/spirea/growing-spirea-shrubs.htm

I understand this frustration very well!
These articles may help you.

https://www.gardeningknowhow.com/plant-problems/pests/animals/camouflage-gardening.htm
https://www.gardeningknowhow.com/plant-problems/pests/animals/keep-rabbits-out-of-gardens.htm

Summer Spirea typically blooms from late June until the end of summer. Depending on the variety, spring Spireas can bloom from early to late spring or for a shorter period.

Yes, a Spirea will lose it's leaves each fall.

https://www.gardeningknowhow.com/ornamental/shrubs/spirea/growing-spirea-shrubs.htm

The Spirea has Fire Blight.