The plain-English answer
A solid conservatory roof is any roof that's opaque (not see-through) and fully insulated. A tiled conservatory roof is a solid roof with composite slate-effect or shingle-effect tiles on the outside. Almost every modern solid conservatory roof in the UK is tiled, so the two terms are used interchangeably by installers, manufacturers and homeowners.
When the difference matters
Occasionally "solid roof" is used to describe a flat-roofed extension finish (felt, EPDM rubber, GRP). On a conservatory, that's rare and rarely recommended, pitched composite tiles look better, complement the house, and shed water faster. If an installer offers you a "solid" roof, ask what the external finish actually is. With Smart-Roof it's always a pitched, lightweight composite tile system.
Performance, identical
Whether you call it tiled, solid, warm-roof or insulated-roof, the U-value (0.15–0.18 W/m²K), the rain-noise reduction (down to ~35 dB), the Building Regulations compliance and the lifespan (30+ years) are the same. What matters is the construction underneath, multi-layer insulation, lightweight engineered structure, plastered ceiling, not the marketing word on the brochure.