What is the difference between frame relay and point-to-point?

Frame relay (FR) is a shared connection. Point-to-point (P2P) is a private, non-shared connection.

For P2P, you install a direct private line T1 circuit between the customer's location and the closest ISP's POP (Point of Presence, access point), which is itself connected to the Internet backbone via a P2P connection.  The data pipe is always a full T1.  In order to obtain a fractional T1, the ISP throttles the bandwidth (to say 384K) at the router port.  Increasing bandwidth is a simple router re-configuration. This is the better an more expensive method because the ISP is  paying the Telco for a full T1 pipe that is private (i.e. not shared by anyone else). The cost is in direct relation to the distance between the customer's location and the ISP's P2P connection to the Internet backbone. This is important when comparing ISPs, as some connect their POPs to each other and to their NOC (Network Operations Center) using a Frame Relay network.  In this scenario you may have a P2P connection to the ISP POP, but to the Internet backbone you have a FR connection!

For FR, a circuit is ordered between the customer's location and the FR "cloud" (usually a large Telco CO (Central Office) close to the customer) and a separate circuit between the ISP and the FR "cloud" (usually another large Telco CO close to the ISP's home office).  Within the "cloud", traffic is shared and managed by the Telco.  FR is cheaper because it is shared and because it is not distance-sensitive, is of lesser quality and offers lower standards.  In order to insure quality, FR circuits come with Committed Information Rates (CIR).  The CIR is the guaranteed bandwidth. You may be able to go over it, but you are not guaranteed anything over it.  However,  you are always guaranteed at least the CIR.  The most common FR T1 circuit  is a FR  T1 (up to 1.5Mbs) which comes  with a CIR of 512Kbps.

A P2TP circuit doesn't have a CIR.  What you order is what you get.  A fractional P2P is obtained by throttling the bandwidth at the router port.  In essence you have (and pay for) a full T1 (1.5 Mbps) data pipe that is throttled at the router port  to only allow ,say 384 Kbps of data at all times.  Increasing you bandwidth is a simple re-configuration of the router port speed.

 FR  works best for companies that have an average bandwidth of less than 200 or 300 Kbps with only occasional bursts over 1.0Mbps. Companies that require average bandwidth in excess of 512Kbps (most serious web servers and definitely e-commerce servers) should order a full P2P T1 circuit.

PTP offers the high speed, consistent performance and the best control for e-commerce retailers, web hosting companies and medium to large companies with high bandwidth requirements.  With P2P services, you have a private, exclusive connection from your company to the Internet.  FR allows you to share a line "in the cloud" with other FR customers in order to lower your costs.

P2P is an extremely reliable and tested method of data transport.  P2P circuits are what coined the term T-1, and up until 1996 most data transport was carried on P2P circuits. This type of circuit can be envisioned like throwing a cable from one location to another and using it to connect the two locations.

Because P2P circuits require provisioning of the wire from start to end, there are additional mileage costs.  The further apart the two points of connection are the more expensive the "local loop" will be.