I get frustrated with both the landscape architects (and garden designers) and the nursery industry who cannot tell one genus from another despite lots of research and numerous reminders from horticultural and botanical experts.
Let's try this again.
First plant is NOT Liriope muscari 'Stripey White' - it is Ophiopogon intermedius 'Argenteomarginatus' , sometimes sold as Ophiopogon intermedius 'Albo Marginata'. Note: it has white flowers on a 'flat' stalk.
Leaves appear white along the margins with green down the middle.
Registration for this plant should never have been allowed using the 'Liriope' name.
Second plant is Liriope muscari 'Variegata' and it has blue flowers on a 'round' stalk.
Leaves appear creamy-yellow along the margins with green down the middle.
The Liriope genus tend to preform better in cooler temperate to subtropical climates, though flowers are more prominent in the cooler climate regions - a good COLD winter does indeed improve the flowering.
Ophiopogon intermedius is a wonderful strappy plant to use in gardens and commercial landscape projects. It is considered better adapted to the tropics and subtropics and flowers more reliably compared to other Liriope cultivars such as ‘Monroe’s White’.