Logos needed for two new food businesses

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Logo Design Brief
Four logos required for two new businesses.
Out of the four, we need two main logos for two new food businesses in Scotland.
One is a catering company called Famishd (intentionally spelled without the 'e'). It will deliver freshly homemade lunch options to business premises. The only idea we have had with this one, is to incorporate a fork design into the 'f', but that isn't a requirement of the brief, just an idea.
(Also, there is a Famishd in Australia, easily found with a Google search, so our logo must differ from theirs.)
The second one is a coffee and cake, city center meeting place, called Parchd (again without the 'e'). No ideas with this one.
(And nothing on Google this time either.)
We want it to be obvious that the two businesses are connected, so would like the logos to match each other in some way. This is quite important to us, to establish our brand going forward.
We also require famishd.co.uk and parchd.co.uk sub-logos to accompany the main ones, to use as we establish our web presence. (Bringing the total to four.)
We are looking for something modern. Maybe cleverly minimalist? Something that makes us think "that's cool", while also maintaining a professional image. Ideally they will look good standing alone on a white background, but we'd like the versatility to place them on any colour background.
So pretty open to ideas.... surprise us!
Thank you for your efforts in advance.
Target Market(s)
Famishd - People who are hungry and thirsty at lunchtime.
Parchd - People who would like to indulge in a coffee with a piece of cake, and a chat with friends.
Industry/Entity Type
Catering
Logo Text
Famishd Parchd Famishd.co.uk Parchd.co.uk
Logo styles of interest
Emblem Logo
Logo enclosed in a shape



Abstract Logo
Conceptual / symbolic (optional text)



Wordmark Logo
Word or name based logo (text only)


Font styles to use
Look and feel
Each slider illustrates characteristics of the customer's brand and the style your logo design should communicate.
Elegant
Bold
Playful
Serious
Traditional
Modern
Personable
Professional
Feminine
Masculine
Colorful
Conservative
Economical
Upmarket
Requirements
Must have
- Must match each other in some way. It has to be obvious the two companies are from the same 'family' of companies.
Nice to have
- If the 'f' from Famishd and the 'p' from Parchd, could be usable stand-alone (like Facebook and Twitter do), that would be an added bonus.
Should not have
- Must not be old-fashioned.