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.